kerroinkunta

kerroinkunta (nominative singular)
kerroinkunnat (nominative plural)
kerroinkunta (accusative nominative singular)
kerroinkunnat (accusative nominative plural)
kerroinkunnan (accusative genitive singular)
kerroinkunnat (accusative genitive plural)
kerroinkunnan (genitive singular)
kerroinkuntien (genitive plural)
kerroinkuntain (genitive plural rare)
kerroinkuntaa (partitive singular)
kerroinkuntia (partitive plural)
kerroinkunnassa (inessive singular)
kerroinkunnissa (inessive plural)
kerroinkunnasta (elative singular)
kerroinkunnista (elative plural)
kerroinkuntaan (illative singular)
kerroinkuntiin (illative plural)
kerroinkunnalla (adessive singular)
kerroinkunnilla (adessive plural)
kerroinkunnalta (ablative singular)
kerroinkunnilta (ablative plural)
kerroinkunnalle (allative singular)
kerroinkunnille (allative plural)
kerroinkuntana (essive singular)
kerroinkuntina (essive plural)
kerroinkunnaksi (singular translative)
kerroinkunniksi (plural translative)
kerroinkunnatta (abessive singular)
kerroinkunnitta (abessive plural)
kerroinkunnin (instructive plural)
See the possessive forms below. (comitative)
kerroinkuntani (nominative singular)
kerroinkuntani (nominative plural)
kerroinkuntani (accusative nominative singular)
kerroinkuntani (accusative nominative plural)
kerroinkuntani (accusative genitive singular)
kerroinkuntani (accusative genitive plural)
kerroinkuntani (genitive singular)
kerroinkuntieni (genitive plural)
kerroinkuntaini (genitive plural rare)
kerroinkuntaani (partitive singular)
kerroinkuntiani (partitive plural)
kerroinkunnassani (inessive singular)
kerroinkunnissani (inessive plural)
kerroinkunnastani (elative singular)
kerroinkunnistani (elative plural)
kerroinkuntaani (illative singular)
kerroinkuntiini (illative plural)
kerroinkunnallani (adessive singular)
kerroinkunnillani (adessive plural)
kerroinkunnaltani (ablative singular)
kerroinkunniltani (ablative plural)
kerroinkunnalleni (allative singular)
kerroinkunnilleni (allative plural)
kerroinkuntanani (essive singular)
kerroinkuntinani (essive plural)
kerroinkunnakseni (singular translative)
kerroinkunnikseni (plural translative)
kerroinkunnattani (abessive singular)
kerroinkunnittani (abessive plural)
kerroinkuntineni (comitative plural)
kerroinkuntasi (nominative singular)
kerroinkuntasi (nominative plural)
kerroinkuntasi (accusative nominative singular)
kerroinkuntasi (accusative nominative plural)
kerroinkuntasi (accusative genitive singular)
kerroinkuntasi (accusative genitive plural)
kerroinkuntasi (genitive singular)
kerroinkuntiesi (genitive plural)
kerroinkuntaisi (genitive plural rare)
kerroinkuntaasi (partitive singular)
kerroinkuntiasi (partitive plural)
kerroinkunnassasi (inessive singular)
kerroinkunnissasi (inessive plural)
kerroinkunnastasi (elative singular)
kerroinkunnistasi (elative plural)
kerroinkuntaasi (illative singular)
kerroinkuntiisi (illative plural)
kerroinkunnallasi (adessive singular)
kerroinkunnillasi (adessive plural)
kerroinkunnaltasi (ablative singular)
kerroinkunniltasi (ablative plural)
kerroinkunnallesi (allative singular)
kerroinkunnillesi (allative plural)
kerroinkuntanasi (essive singular)
kerroinkuntinasi (essive plural)
kerroinkunnaksesi (singular translative)
kerroinkunniksesi (plural translative)
kerroinkunnattasi (abessive singular)
kerroinkunnittasi (abessive plural)
kerroinkuntinesi (comitative plural)
kerroinkuntamme (nominative singular)
kerroinkuntamme (nominative plural)
kerroinkuntamme (accusative nominative singular)
kerroinkuntamme (accusative nominative plural)
kerroinkuntamme (accusative genitive singular)
kerroinkuntamme (accusative genitive plural)
kerroinkuntamme (genitive singular)
kerroinkuntiemme (genitive plural)
kerroinkuntaimme (genitive plural rare)
kerroinkuntaamme (partitive singular)
kerroinkuntiamme (partitive plural)
kerroinkunnassamme (inessive singular)
kerroinkunnissamme (inessive plural)
kerroinkunnastamme (elative singular)
kerroinkunnistamme (elative plural)
kerroinkuntaamme (illative singular)
kerroinkuntiimme (illative plural)
kerroinkunnallamme (adessive singular)
kerroinkunnillamme (adessive plural)
kerroinkunnaltamme (ablative singular)
kerroinkunniltamme (ablative plural)
kerroinkunnallemme (allative singular)
kerroinkunnillemme (allative plural)
kerroinkuntanamme (essive singular)
kerroinkuntinamme (essive plural)
kerroinkunnaksemme (singular translative)
kerroinkunniksemme (plural translative)
kerroinkunnattamme (abessive singular)
kerroinkunnittamme (abessive plural)
kerroinkuntinemme (comitative plural)
kerroinkuntanne (nominative singular)
kerroinkuntanne (nominative plural)
kerroinkuntanne (accusative nominative singular)
kerroinkuntanne (accusative nominative plural)
kerroinkuntanne (accusative genitive singular)
kerroinkuntanne (accusative genitive plural)
kerroinkuntanne (genitive singular)
kerroinkuntienne (genitive plural)
kerroinkuntainne (genitive plural rare)
kerroinkuntaanne (partitive singular)
kerroinkuntianne (partitive plural)
kerroinkunnassanne (inessive singular)
kerroinkunnissanne (inessive plural)
kerroinkunnastanne (elative singular)
kerroinkunnistanne (elative plural)
kerroinkuntaanne (illative singular)
kerroinkuntiinne (illative plural)
kerroinkunnallanne (adessive singular)
kerroinkunnillanne (adessive plural)
kerroinkunnaltanne (ablative singular)
kerroinkunniltanne (ablative plural)
kerroinkunnallenne (allative singular)
kerroinkunnillenne (allative plural)
kerroinkuntananne (essive singular)
kerroinkuntinanne (essive plural)
kerroinkunnaksenne (singular translative)
kerroinkunniksenne (plural translative)
kerroinkunnattanne (abessive singular)
kerroinkunnittanne (abessive plural)
kerroinkuntinenne (comitative plural)
kerroinkuntansa (nominative singular)
kerroinkuntansa (nominative plural)
kerroinkuntansa (accusative nominative singular)
kerroinkuntansa (accusative nominative plural)
kerroinkuntansa (accusative genitive singular)
kerroinkuntansa (accusative genitive plural)
kerroinkuntansa (genitive singular)
kerroinkuntiensa (genitive plural)
kerroinkuntainsa (genitive plural rare)
kerroinkuntaansa (partitive singular)
kerroinkuntiaan (partitive plural)
kerroinkuntiansa (partitive plural)
kerroinkunnassaan (inessive singular)
kerroinkunnassansa (inessive singular)
kerroinkunnissaan (inessive plural)
kerroinkunnissansa (inessive plural)
kerroinkunnastaan (elative singular)
kerroinkunnastansa (elative singular)
kerroinkunnistaan (elative plural)
kerroinkunnistansa (elative plural)
kerroinkuntaansa (illative singular)
kerroinkuntiinsa (illative plural)
kerroinkunnallaan (adessive singular)
kerroinkunnallansa (adessive singular)
kerroinkunnillaan (adessive plural)
kerroinkunnillansa (adessive plural)
kerroinkunnaltaan (ablative singular)
kerroinkunnaltansa (ablative singular)
kerroinkunniltaan (ablative plural)
kerroinkunniltansa (ablative plural)
kerroinkunnalleen (allative singular)
kerroinkunnallensa (allative singular)
kerroinkunnilleen (allative plural)
kerroinkunnillensa (allative plural)
kerroinkuntanaan (essive singular)
kerroinkuntanansa (essive singular)
kerroinkuntinaan (essive plural)
kerroinkuntinansa (essive plural)
kerroinkunnakseen (singular translative)
kerroinkunnaksensa (singular translative)
kerroinkunnikseen (plural translative)
kerroinkunniksensa (plural translative)
kerroinkunnattaan (abessive singular)
kerroinkunnattansa (abessive singular)
kerroinkunnittaan (abessive plural)
kerroinkunnittansa (abessive plural)
kerroinkuntineen (comitative plural)
kerroinkuntinensa (comitative plural)

[ˈk̟e̞rːo̞i̯ŋˌkun̪t̪ɑ̝]


Kummer ring

Named after Ernst Kummer (1810–1893), a German mathematician.

(algebra) A ring obtained by adjoining a non-real complex pᵗʰ root of unity (where p is a prime number) to the ring of integers.


Zahlenkörper

de-noun

Zahlenkörper m (strong, genitive Zahlenkörpers, plural Zahlenkörper)

Zahlenkörpers (genitive)
Zahlenkörper (plural)
Zahlenkörper (nominative singular)
Zahlenkörper (definite nominative plural)
Zahlenkörpers (genitive singular)
Zahlenkörper (definite genitive plural)
Zahlenkörper (dative singular)
Zahlenkörpern (dative definite plural)
Zahlenkörper (accusative singular)
Zahlenkörper (accusative definite plural)

From Zahl (“number”) + -en- + Körper (“body”).

compound

algebraic number field
algebraic number field

(mathematics, algebra) algebraic number field


simple extension

en-noun

simple extension (plural simple extensions)

(algebra, field theory) A field extension obtained by adjoining a single element to a given field.


root field

(algebra, Galois theory) splitting field


ring of fractions

ring of fractions (plural rings of fractions)

(algebra) A ring whose elements are fractions whose numerators belong to a given commutative unital ring and whose denominators belong to a multiplicatively closed unital subset D of that given ring. Addition and multiplication of such fractions is defined just as for a field of fractions. A pair of fractions a/b and c/d are deemed equivalent if there is a member x of D such that x(ad-bc)=0.


total ring of fractions

total ring of fractions (plural total rings of fractions)

(algebra) A ring of fractions of a given ring, such that the set of allowed denominators contains all of the non-zero divisors of the given ring.


separable extension

separable extension (plural separable extensions)

separable polynomial
separable polynomial

(algebra) A finite (and thereby algebraic) extension of a base field such that every element of the extension is the root of a separable polynomial over the base field.


normal extension

normal extension (plural normal extensions)

(algebra) A finite, algebraic extension of some field such that if it contains any root of any irreducible polynomial over that base field then it contains all of the roots of that polynomial.


fixed field

(algebra, Galois theory) A subfield of a given field which contains all of the fixed points that are common to all of the automorphisms of some subgroup of the automorphism group of that given field.


simple root

(algebra) A root of a polynomial equation which has multiplicity one.


multiple root

(algebra) A root of a polynomial equation which has multiplicity greater than one.


ẩn số

[ʔən˧˩ so˧˦]

[ʔəŋ˧˨ ʂow˨˩˦]

[ʔəŋ˧˨ sow˨˩˦]

[ʔəŋ˨˩˦ ʂow˦˥]

[ʔəŋ˨˩˦ sow˦˥]

Sino-Vietnamese word from 隱 (“to hide”) and 數 (“number”)


Rolle-féle gyöktétel

Rolle (“Rolle”) + -féle (“’s, by”) + gyöktétel (“root theorem”), literally “Rolle's root theorem”.

rational root theorem
rational root theorem


solvable group

(algebra, Galois theory) A group G which is part of a finite chain Gᵢ (0 ≤ i ≤ n) of subgroups, where G₀ is the trivial subgroup and Gₙ = G, such that each intermediate subgroup Gᵢ is a normal subgroup of the next in the chain (i.e., Gᵢ ◁ Gᵢ₊₁) and each quotient Gᵢ₊₁/Gᵢ is a cyclic group.


k-algebra

A k'''-algebra A with ring homomorphism ϕ:k→A is a k-vector space with scalar multiplication (i.e., action of k upon A): λ·a=ϕ(λ)a where λ∈k,a∈A.

algebra over a field
algebra over a field

(algebra) An algebra over a field; a ring with identity together with an injective ring homomorphism from a field, k, to the ring such that the image of the field is a subset of the center of the ring and such that the image of the field’s unity is the ring’s unity.


direct system

(algebra) A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset.


direct limit

A direct limit has “canonical functions” which map each element of the disjoint union to its equivalence class.

Direct limits in the algebraic sense are models of category-theoretic colimits.

(algebra) A set of equivalence classes which partition the disjoint union of the members of a direct system; each equivalence class being a sort of “drainage basin” of the mappings (of the morphisms) of the direct system, if these are analogically considered as “rivers”. (If i<k,j<k in the indexing poset, then there exist f_ik:A_i→A_k and f_jk:A_j→A_k. If a_i∈A_i,a_j∈A_j such that f_ik(a_i)=f_jk(a_j) then a_i∼a_j. If k = j then f_jj(a_j)=a_j,f_ij(a_i)=a_j.)


projective module

en-noun

projective module (plural projective modules)

(algebra) A module which is a direct summand of a free module.


Noetherian module

Noetherian module (plural Noetherian modules)

Noetherian modules (plural)
noetherian module (alternative)

(algebra) A module whose every submodule is finitely generated; or equivalently, a module whose submodules satisfy an ascending chain condition (i.e., any ascending chain of submodules levels off after a finite number of steps).


regular element

regular element (plural regular elements)

(algebra) An element of a ring that is not a zero divisor.


deskonposizio gorputz

deskonposizio gorputz (absolutive indefinite)
deskonposizio gorputza (absolutive indefinite singular)
deskonposizio gorputzak (absolutive indefinite plural)
deskonposizio gorputzek (ergative indefinite)
deskonposizio gorputzak (ergative indefinite singular)
deskonposizio gorputzek (ergative indefinite plural)
deskonposizio gorputzi (dative indefinite)
deskonposizio gorputzari (dative indefinite singular)
deskonposizio gorputzei (dative indefinite plural)
deskonposizio gorputzen (genitive indefinite)
deskonposizio gorputzaren (genitive indefinite singular)
deskonposizio gorputzen (genitive indefinite plural)
deskonposizio gorputzekin (comitative indefinite)
deskonposizio gorputzarekin (comitative indefinite singular)
deskonposizio gorputzekin (comitative indefinite plural)
deskonposizio gorputzengatik (causative indefinite)
deskonposizio gorputzarengatik (causative indefinite singular)
deskonposizio gorputzengatik (causative indefinite plural)
deskonposizio gorputzentzat (benefactive indefinite)
deskonposizio gorputzarentzat (benefactive indefinite singular)
deskonposizio gorputzentzat (benefactive indefinite plural)
deskonposizio gorputzez (indefinite instrumental)
deskonposizio gorputzaz (indefinite instrumental singular)
deskonposizio gorputzez (indefinite instrumental plural)
deskonposizio gorputzetan (indefinite inessive)
deskonposizio gorputzean (indefinite inessive singular)
deskonposizio gorputzetan (indefinite inessive plural)
deskonposizio gorputzetako (indefinite locative)
deskonposizio gorputzeko (indefinite locative singular)
deskonposizio gorputzetako (indefinite locative plural)
deskonposizio gorputzetara (allative indefinite)
deskonposizio gorputzera (allative indefinite singular)
deskonposizio gorputzetara (allative indefinite plural)
deskonposizio gorputzetaraino (indefinite terminative)
deskonposizio gorputzeraino (indefinite singular terminative)
deskonposizio gorputzetaraino (indefinite plural terminative)
deskonposizio gorputzetarantz (directive indefinite)
deskonposizio gorputzerantz (directive indefinite singular)
deskonposizio gorputzetarantz (directive indefinite plural)
deskonposizio gorputzetarako (destinative indefinite)
deskonposizio gorputzerako (destinative indefinite singular)
deskonposizio gorputzetarako (destinative indefinite plural)
deskonposizio gorputzetatik (ablative indefinite)
deskonposizio gorputzetik (ablative indefinite singular)
deskonposizio gorputzetatik (ablative indefinite plural)
deskonposizio gorputzik (indefinite partitive)
deskonposizio gorpuztzat (indefinite prolative)

(algebra, Galois theory) (of a polynomial) splitting field


banatze gorputz

banatze gorputz (absolutive indefinite)
banatze gorputza (absolutive indefinite singular)
banatze gorputzak (absolutive indefinite plural)
banatze gorputzek (ergative indefinite)
banatze gorputzak (ergative indefinite singular)
banatze gorputzek (ergative indefinite plural)
banatze gorputzi (dative indefinite)
banatze gorputzari (dative indefinite singular)
banatze gorputzei (dative indefinite plural)
banatze gorputzen (genitive indefinite)
banatze gorputzaren (genitive indefinite singular)
banatze gorputzen (genitive indefinite plural)
banatze gorputzekin (comitative indefinite)
banatze gorputzarekin (comitative indefinite singular)
banatze gorputzekin (comitative indefinite plural)
banatze gorputzengatik (causative indefinite)
banatze gorputzarengatik (causative indefinite singular)
banatze gorputzengatik (causative indefinite plural)
banatze gorputzentzat (benefactive indefinite)
banatze gorputzarentzat (benefactive indefinite singular)
banatze gorputzentzat (benefactive indefinite plural)
banatze gorputzez (indefinite instrumental)
banatze gorputzaz (indefinite instrumental singular)
banatze gorputzez (indefinite instrumental plural)
banatze gorputzetan (indefinite inessive)
banatze gorputzean (indefinite inessive singular)
banatze gorputzetan (indefinite inessive plural)
banatze gorputzetako (indefinite locative)
banatze gorputzeko (indefinite locative singular)
banatze gorputzetako (indefinite locative plural)
banatze gorputzetara (allative indefinite)
banatze gorputzera (allative indefinite singular)
banatze gorputzetara (allative indefinite plural)
banatze gorputzetaraino (indefinite terminative)
banatze gorputzeraino (indefinite singular terminative)
banatze gorputzetaraino (indefinite plural terminative)
banatze gorputzetarantz (directive indefinite)
banatze gorputzerantz (directive indefinite singular)
banatze gorputzetarantz (directive indefinite plural)
banatze gorputzetarako (destinative indefinite)
banatze gorputzerako (destinative indefinite singular)
banatze gorputzetarako (destinative indefinite plural)
banatze gorputzetatik (ablative indefinite)
banatze gorputzetik (ablative indefinite singular)
banatze gorputzetatik (ablative indefinite plural)
banatze gorputzik (indefinite partitive)
banatze gorpuztzat (indefinite prolative)


banatu

eu-verb

banatu ? (imperfect participle banatzen, future participle banatuko, short form bana, verbal noun banatze)

banatzen (imperfect participle)
banatuko (future participle)
bana (short-form)
banatze (noun-from-verb)

(algebra, acts on a polynomial) To split.


trùng phương

[t͡ɕʊwŋ͡m˨˩ fɨəŋ˧˧]

[ʈʊwŋ͡m˦˩ fɨəŋ˧˧]

[ʈʊwŋ͡m˨˩ fɨəŋ˧˧]

Perhaps Sino-Vietnamese word from 重 and 方, as in a blend of trùng lặp (“to compound”) + bình phương (“square”), as in "compounding a square raises the power to 4".

blend

(algebra, of a phương trình (“equation”)) biquadratic (with only the 4th and 2nd powers)


超越次數

ㄔㄠ ㄩㄝˋ ㄘˋ ㄕㄨˋ

ㄔㄠ ㄩㄝˋ ㄘˋ ㄕㄨˋ

/ʈ͡ʂʰɑʊ̯⁵⁵ ɥɛ⁵¹⁻⁵³ t͡sʰz̩⁵¹⁻⁵³ ʂu⁵¹/

/ʈ͡ʂʰɑʊ̯⁵⁵ ɥɛ⁵¹⁻⁵³ t͡sʰz̩⁵¹⁻⁵³ ʂu⁵¹/

Particularly, the extension field of K is algebraic if and only if its transcendence degree on K is zero.

2003, 朱尧辰 (Zhu Yaochen), 徐广善 (Xu Guangshan), 《超越数引论》 [Introduction to Transcendental Number]

Tèbié, K de kuòyù shì dàishù de, dāngqiějǐndāng tā zài K shàng de chāoyuè cìshù wèi líng.

特別，K的擴域是代數的，當且僅當它在K上的超越次數為零。

特别，K的扩域是代数的，当且仅当它在K上的超越次数为零。

transcendence degree
transcendence degree

(algebra, field theory, of a field extension) transcendence degree


ausklammern

de-verb

ausklammern (weak, third-person singular present klammert aus, past tense klammerte aus, past participle ausgeklammert, auxiliary haben)

klammert aus (present singular third-person)
klammerte aus (past)
ausgeklammert (participle past)
haben (auxiliary)
haben (auxiliary)
ausklammern (infinitive)
ausklammernd (participle present)
ausgeklammert (participle past)
auszuklammern (infinitive infinitive-zu)
klammre aus (first-person indicative present singular)
klammere aus (first-person indicative present singular)
klammer aus (first-person indicative present singular)
klammern aus (first-person indicative plural present)
klammere aus (first-person singular subjunctive subjunctive-i)
klammre aus (first-person singular subjunctive subjunctive-i)
klammern aus (first-person plural subjunctive subjunctive-i)
klammerst aus (indicative present second-person singular)
klammert aus (indicative plural present second-person)
klammerest aus (second-person singular subjunctive subjunctive-i)
klammrest aus (second-person singular subjunctive subjunctive-i)
klammeret aus (plural second-person subjunctive subjunctive-i)
klammret aus (plural second-person subjunctive subjunctive-i)
klammert aus (indicative present singular third-person)
klammern aus (indicative plural present third-person)
klammere aus (singular subjunctive subjunctive-i third-person)
klammre aus (singular subjunctive subjunctive-i third-person)
klammern aus (plural subjunctive subjunctive-i third-person)
klammerte aus (first-person indicative preterite singular)
klammerten aus (first-person indicative plural preterite)
klammerte aus (first-person formal rare singular subjunctive subjunctive-ii)
klammerten aus (first-person formal plural rare subjunctive subjunctive-ii)
klammertest aus (indicative preterite second-person singular)
klammertet aus (indicative plural preterite second-person)
klammertest aus (formal rare second-person singular subjunctive subjunctive-ii)
klammertet aus (formal plural rare second-person subjunctive subjunctive-ii)
klammerte aus (indicative preterite singular third-person)
klammerten aus (indicative plural preterite third-person)
klammerte aus (formal rare singular subjunctive subjunctive-ii third-person)
klammerten aus (formal plural rare subjunctive subjunctive-ii third-person)
klammre aus (imperative second-person singular)
klammer aus (imperative second-person singular)
klammere aus (imperative second-person singular)
klammert aus (imperative plural second-person)
haben (auxiliary)
ausklammre (first-person indicative present singular subordinate-clause)
ausklammere (first-person indicative present singular subordinate-clause)
ausklammer (first-person indicative present singular subordinate-clause)
ausklammern (first-person indicative plural present subordinate-clause)
ausklammere (first-person singular subjunctive subjunctive-i subordinate-clause)
ausklammre (first-person singular subjunctive subjunctive-i subordinate-clause)
ausklammern (first-person plural subjunctive subjunctive-i subordinate-clause)
ausklammerst (indicative present second-person singular subordinate-clause)
ausklammert (indicative plural present second-person subordinate-clause)
ausklammerest (second-person singular subjunctive subjunctive-i subordinate-clause)
ausklammrest (second-person singular subjunctive subjunctive-i subordinate-clause)
ausklammeret (plural second-person subjunctive subjunctive-i subordinate-clause)
ausklammret (plural second-person subjunctive subjunctive-i subordinate-clause)
ausklammert (indicative present singular subordinate-clause third-person)
ausklammern (indicative plural present subordinate-clause third-person)
ausklammere (singular subjunctive subjunctive-i subordinate-clause third-person)
ausklammre (singular subjunctive subjunctive-i subordinate-clause third-person)
ausklammern (plural subjunctive subjunctive-i subordinate-clause third-person)
ausklammerte (first-person indicative preterite singular subordinate-clause)
ausklammerten (first-person indicative plural preterite subordinate-clause)
ausklammerte (first-person formal rare singular subjunctive subjunctive-ii subordinate-clause)
ausklammerten (first-person formal plural rare subjunctive subjunctive-ii subordinate-clause)
ausklammertest (indicative preterite second-person singular subordinate-clause)
ausklammertet (indicative plural preterite second-person subordinate-clause)
ausklammertest (formal rare second-person singular subjunctive subjunctive-ii subordinate-clause)
ausklammertet (formal plural rare second-person subjunctive subjunctive-ii subordinate-clause)
ausklammerte (indicative preterite singular subordinate-clause third-person)
ausklammerten (indicative plural preterite subordinate-clause third-person)
ausklammerte (formal rare singular subjunctive subjunctive-ii subordinate-clause third-person)
ausklammerten (formal plural rare subjunctive subjunctive-ii subordinate-clause third-person)
haben (auxiliary)
habe ausgeklammert (first-person indicative multiword-construction perfect singular)
haben ausgeklammert (first-person indicative multiword-construction perfect plural)
habe ausgeklammert (first-person multiword-construction perfect singular subjunctive)
haben ausgeklammert (first-person multiword-construction perfect plural subjunctive)
hast ausgeklammert (indicative multiword-construction perfect second-person singular)
habt ausgeklammert (indicative multiword-construction perfect plural second-person)
habest ausgeklammert (multiword-construction perfect second-person singular subjunctive)
habet ausgeklammert (multiword-construction perfect plural second-person subjunctive)
hat ausgeklammert (indicative multiword-construction perfect singular third-person)
haben ausgeklammert (indicative multiword-construction perfect plural third-person)
habe ausgeklammert (multiword-construction perfect singular subjunctive third-person)
haben ausgeklammert (multiword-construction perfect plural subjunctive third-person)
hatte ausgeklammert (first-person indicative multiword-construction pluperfect singular)
hatten ausgeklammert (first-person indicative multiword-construction pluperfect plural)
hätte ausgeklammert (first-person multiword-construction pluperfect singular subjunctive)
hätten ausgeklammert (first-person multiword-construction pluperfect plural subjunctive)
hattest ausgeklammert (indicative multiword-construction pluperfect second-person singular)
hattet ausgeklammert (indicative multiword-construction pluperfect plural second-person)
hättest ausgeklammert (multiword-construction pluperfect second-person singular subjunctive)
hättet ausgeklammert (multiword-construction pluperfect plural second-person subjunctive)
hatte ausgeklammert (indicative multiword-construction pluperfect singular third-person)
hatten ausgeklammert (indicative multiword-construction pluperfect plural third-person)
hätte ausgeklammert (multiword-construction pluperfect singular subjunctive third-person)
hätten ausgeklammert (multiword-construction pluperfect plural subjunctive third-person)
ausklammern werden (future future-i infinitive multiword-construction)
werde ausklammern (first-person future future-i multiword-construction singular subjunctive subjunctive-i)
werden ausklammern (first-person future future-i multiword-construction plural subjunctive subjunctive-i)
werdest ausklammern (future future-i multiword-construction second-person singular subjunctive subjunctive-i)
werdet ausklammern (future future-i multiword-construction plural second-person subjunctive subjunctive-i)
werde ausklammern (future future-i multiword-construction singular subjunctive subjunctive-i third-person)
werden ausklammern (future future-i multiword-construction plural subjunctive subjunctive-i third-person)
werde ausklammern (first-person future future-i indicative multiword-construction singular)
werden ausklammern (first-person future future-i indicative multiword-construction plural)
würde ausklammern (first-person future future-i multiword-construction singular subjunctive subjunctive-ii)
würden ausklammern (first-person future future-i multiword-construction plural subjunctive subjunctive-ii)
wirst ausklammern (future future-i indicative multiword-construction second-person singular)
werdet ausklammern (future future-i indicative multiword-construction plural second-person)
würdest ausklammern (future future-i multiword-construction second-person singular subjunctive subjunctive-ii)
würdet ausklammern (future future-i multiword-construction plural second-person subjunctive subjunctive-ii)
wird ausklammern (future future-i indicative multiword-construction singular third-person)
werden ausklammern (future future-i indicative multiword-construction plural third-person)
würde ausklammern (future future-i multiword-construction singular subjunctive subjunctive-ii third-person)
würden ausklammern (future future-i multiword-construction plural subjunctive subjunctive-ii third-person)
ausgeklammert haben werden (future future-ii infinitive multiword-construction)
werde ausgeklammert haben (first-person future future-ii multiword-construction singular subjunctive subjunctive-i)
werden ausgeklammert haben (first-person future future-ii multiword-construction plural subjunctive subjunctive-i)
werdest ausgeklammert haben (future future-ii multiword-construction second-person singular subjunctive subjunctive-i)
werdet ausgeklammert haben (future future-ii multiword-construction plural second-person subjunctive subjunctive-i)
werde ausgeklammert haben (future future-ii multiword-construction singular subjunctive subjunctive-i third-person)
werden ausgeklammert haben (future future-ii multiword-construction plural subjunctive subjunctive-i third-person)
werde ausgeklammert haben (first-person future future-ii indicative multiword-construction singular)
werden ausgeklammert haben (first-person future future-ii indicative multiword-construction plural)
würde ausgeklammert haben (first-person future future-ii multiword-construction singular subjunctive subjunctive-ii)
würden ausgeklammert haben (first-person future future-ii multiword-construction plural subjunctive subjunctive-ii)
wirst ausgeklammert haben (future future-ii indicative multiword-construction second-person singular)
werdet ausgeklammert haben (future future-ii indicative multiword-construction plural second-person)
würdest ausgeklammert haben (future future-ii multiword-construction second-person singular subjunctive subjunctive-ii)
würdet ausgeklammert haben (future future-ii multiword-construction plural second-person subjunctive subjunctive-ii)
wird ausgeklammert haben (future future-ii indicative multiword-construction singular third-person)
werden ausgeklammert haben (future future-ii indicative multiword-construction plural third-person)
würde ausgeklammert haben (future future-ii multiword-construction singular subjunctive subjunctive-ii third-person)
würden ausgeklammert haben (future future-ii multiword-construction plural subjunctive subjunctive-ii third-person)

Im Ausdruck 2x²−4x, kann man 2x ausklammern

In the expression 2x²−4x, you can factor out 2x

(mathematics, algebra) to factor out; isolate a common factor from an expression


Euclid's lemma

Named after ancient Greek mathematician Euclid of Alexandria (fl. 300 BCE). A version of the proposition appears in Book VII of his Elements.

principal ideal domain
principal ideal domain

(number theory) The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;

The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;
slightly more generally, the proposition that for integers a, b, c, if a divides bc and gcd(a, b) = 1, then a divides c;
(algebra, by generalisation) the proposition that for elements a, b, c of a given principal ideal domain, if a divides bc and gcd(a, b) = 1, then a divides c.


algebraisk struktur

algebraisk struktur (indefinite nominative singular)
den algebraiske struktur (definite nominative singular)
algebraiske strukturer (indefinite nominative plural)
de algebraiske strukturer (definite nominative plural)
algebraisk strukturs (genitive indefinite singular)
den algebraiske strukturs (definite genitive singular)
algebraiske strukturers (genitive indefinite plural)
de algebraiske strukturers (definite genitive plural)

(countable, algebra) algebraic structure


शोधक

śodhak (romanization)
शोधक (direct singular)
शोधक (direct plural)
शोधक (oblique singular)
शोधकों (oblique plural)
शोधक (singular vocative)
शोधको (plural vocative)

Learned borrowing from Sanskrit शोधक (śodhaka).

lbor

(arithmetic, algebra) the subtrahend, the quantity to be subtracted from a number (to render it capable of yielding an exact square root)


शोधक

śodhaka (romanization)
शोधकः (nominative singular)
शोधकौ (dual nominative)
शोधका1 (dual nominative)
शोधकाः (nominative plural)
शोधकासः1 (nominative plural)
शोधकम् (accusative singular)
शोधकौ (accusative dual)
शोधका1 (accusative dual)
शोधकान् (accusative plural)
शोधकेन (instrumental singular)
शोधकाभ्याम् (dual instrumental)
शोधकैः (instrumental plural)
शोधकेभिः1 (instrumental plural)
शोधकाय (dative singular)
शोधकाभ्याम् (dative dual)
शोधकेभ्यः (dative plural)
शोधकात् (ablative singular)
शोधकाभ्याम् (ablative dual)
शोधकेभ्यः (ablative plural)
शोधकस्य (genitive singular)
शोधकयोः (dual genitive)
शोधकानाम् (genitive plural)
शोधके (locative singular)
शोधकयोः (dual locative)
शोधकेषु (locative plural)
शोधक (singular vocative)
शोधकौ (dual vocative)
शोधका1 (dual vocative)
शोधकाः (plural vocative)
शोधकासः1 (plural vocative)

From the root शुध् (śudh, “to be cleared or cleansed or purified, become pure”) + -अक (-aka).

sa-root

(arithmetic, algebra) "corrector", the subtrahend, the quantity to be subtracted from a number (to render it capable of yielding an exact square root)


algebraic combinatorics

1982, Trevor Evans, Finite Representations of Two-variable Identities, E. Mendelsohn, Algebraic and Geometric Combinatorics, North-Holland, page 135,
It is part of the folklore of algebraic combinatorics that “most' two-variable groupoid identities have non-trivial models in finite fields, the groupoid operation being represented by a linear function ax+by.

This volume arose through the initiative of Kluwer Academic Publishers in an attempt to introduce some areas of research in algebraic combinatorics which originally appeared in Russian to a wider mathematical community.

1993, I. A. Faradžev, A. A. Ivanov, M. Klin, A. J. Woldar, editors, Investigations in Algebraic Theory of Combinatorial Objects, Kluwer Academic, page vii:

This book is intended primarily as a one-semester undergraduate text for a course in algebraic combinatorics.[…]Algebraic combinatorics is a huge subject, so some selection process was necessary to obtain the present text.

2013, Richard P. Stanley, Algebraic Combinatorics, 2nd edition, Springer, page xi:

(algebra, combinatorics) A branch of mathematics in which techniques from abstract algebra are applied to problems in combinatorics, and vice versa.

combinatoire algébrique

branch of mathematics at the intersection of combinatorics and algebra


samanmuotoisuus

samanmuotoisuus (nominative singular)
samanmuotoisuudet (nominative plural)
samanmuotoisuus (accusative nominative singular)
samanmuotoisuudet (accusative nominative plural)
samanmuotoisuuden (accusative genitive singular)
samanmuotoisuudet (accusative genitive plural)
samanmuotoisuuden (genitive singular)
samanmuotoisuuksien (genitive plural)
samanmuotoisuutta (partitive singular)
samanmuotoisuuksia (partitive plural)
samanmuotoisuudessa (inessive singular)
samanmuotoisuuksissa (inessive plural)
samanmuotoisuudesta (elative singular)
samanmuotoisuuksista (elative plural)
samanmuotoisuuteen (illative singular)
samanmuotoisuuksiin (illative plural)
samanmuotoisuudella (adessive singular)
samanmuotoisuuksilla (adessive plural)
samanmuotoisuudelta (ablative singular)
samanmuotoisuuksilta (ablative plural)
samanmuotoisuudelle (allative singular)
samanmuotoisuuksille (allative plural)
samanmuotoisuutena (essive singular)
samanmuotoisuuksina (essive plural)
samanmuotoisuudeksi (singular translative)
samanmuotoisuuksiksi (plural translative)
samanmuotoisuudetta (abessive singular)
samanmuotoisuuksitta (abessive plural)
samanmuotoisuuksin (instructive plural)
See the possessive forms below. (comitative)
samanmuotoisuuteni (nominative singular)
samanmuotoisuuteni (nominative plural)
samanmuotoisuuteni (accusative nominative singular)
samanmuotoisuuteni (accusative nominative plural)
samanmuotoisuuteni (accusative genitive singular)
samanmuotoisuuteni (accusative genitive plural)
samanmuotoisuuteni (genitive singular)
samanmuotoisuuksieni (genitive plural)
samanmuotoisuuttani (partitive singular)
samanmuotoisuuksiani (partitive plural)
samanmuotoisuudessani (inessive singular)
samanmuotoisuuksissani (inessive plural)
samanmuotoisuudestani (elative singular)
samanmuotoisuuksistani (elative plural)
samanmuotoisuuteeni (illative singular)
samanmuotoisuuksiini (illative plural)
samanmuotoisuudellani (adessive singular)
samanmuotoisuuksillani (adessive plural)
samanmuotoisuudeltani (ablative singular)
samanmuotoisuuksiltani (ablative plural)
samanmuotoisuudelleni (allative singular)
samanmuotoisuuksilleni (allative plural)
samanmuotoisuutenani (essive singular)
samanmuotoisuuksinani (essive plural)
samanmuotoisuudekseni (singular translative)
samanmuotoisuuksikseni (plural translative)
samanmuotoisuudettani (abessive singular)
samanmuotoisuuksittani (abessive plural)
samanmuotoisuuksineni (comitative plural)
samanmuotoisuutesi (nominative singular)
samanmuotoisuutesi (nominative plural)
samanmuotoisuutesi (accusative nominative singular)
samanmuotoisuutesi (accusative nominative plural)
samanmuotoisuutesi (accusative genitive singular)
samanmuotoisuutesi (accusative genitive plural)
samanmuotoisuutesi (genitive singular)
samanmuotoisuuksiesi (genitive plural)
samanmuotoisuuttasi (partitive singular)
samanmuotoisuuksiasi (partitive plural)
samanmuotoisuudessasi (inessive singular)
samanmuotoisuuksissasi (inessive plural)
samanmuotoisuudestasi (elative singular)
samanmuotoisuuksistasi (elative plural)
samanmuotoisuuteesi (illative singular)
samanmuotoisuuksiisi (illative plural)
samanmuotoisuudellasi (adessive singular)
samanmuotoisuuksillasi (adessive plural)
samanmuotoisuudeltasi (ablative singular)
samanmuotoisuuksiltasi (ablative plural)
samanmuotoisuudellesi (allative singular)
samanmuotoisuuksillesi (allative plural)
samanmuotoisuutenasi (essive singular)
samanmuotoisuuksinasi (essive plural)
samanmuotoisuudeksesi (singular translative)
samanmuotoisuuksiksesi (plural translative)
samanmuotoisuudettasi (abessive singular)
samanmuotoisuuksittasi (abessive plural)
samanmuotoisuuksinesi (comitative plural)
samanmuotoisuutemme (nominative singular)
samanmuotoisuutemme (nominative plural)
samanmuotoisuutemme (accusative nominative singular)
samanmuotoisuutemme (accusative nominative plural)
samanmuotoisuutemme (accusative genitive singular)
samanmuotoisuutemme (accusative genitive plural)
samanmuotoisuutemme (genitive singular)
samanmuotoisuuksiemme (genitive plural)
samanmuotoisuuttamme (partitive singular)
samanmuotoisuuksiamme (partitive plural)
samanmuotoisuudessamme (inessive singular)
samanmuotoisuuksissamme (inessive plural)
samanmuotoisuudestamme (elative singular)
samanmuotoisuuksistamme (elative plural)
samanmuotoisuuteemme (illative singular)
samanmuotoisuuksiimme (illative plural)
samanmuotoisuudellamme (adessive singular)
samanmuotoisuuksillamme (adessive plural)
samanmuotoisuudeltamme (ablative singular)
samanmuotoisuuksiltamme (ablative plural)
samanmuotoisuudellemme (allative singular)
samanmuotoisuuksillemme (allative plural)
samanmuotoisuutenamme (essive singular)
samanmuotoisuuksinamme (essive plural)
samanmuotoisuudeksemme (singular translative)
samanmuotoisuuksiksemme (plural translative)
samanmuotoisuudettamme (abessive singular)
samanmuotoisuuksittamme (abessive plural)
samanmuotoisuuksinemme (comitative plural)
samanmuotoisuutenne (nominative singular)
samanmuotoisuutenne (nominative plural)
samanmuotoisuutenne (accusative nominative singular)
samanmuotoisuutenne (accusative nominative plural)
samanmuotoisuutenne (accusative genitive singular)
samanmuotoisuutenne (accusative genitive plural)
samanmuotoisuutenne (genitive singular)
samanmuotoisuuksienne (genitive plural)
samanmuotoisuuttanne (partitive singular)
samanmuotoisuuksianne (partitive plural)
samanmuotoisuudessanne (inessive singular)
samanmuotoisuuksissanne (inessive plural)
samanmuotoisuudestanne (elative singular)
samanmuotoisuuksistanne (elative plural)
samanmuotoisuuteenne (illative singular)
samanmuotoisuuksiinne (illative plural)
samanmuotoisuudellanne (adessive singular)
samanmuotoisuuksillanne (adessive plural)
samanmuotoisuudeltanne (ablative singular)
samanmuotoisuuksiltanne (ablative plural)
samanmuotoisuudellenne (allative singular)
samanmuotoisuuksillenne (allative plural)
samanmuotoisuutenanne (essive singular)
samanmuotoisuuksinanne (essive plural)
samanmuotoisuudeksenne (singular translative)
samanmuotoisuuksiksenne (plural translative)
samanmuotoisuudettanne (abessive singular)
samanmuotoisuuksittanne (abessive plural)
samanmuotoisuuksinenne (comitative plural)
samanmuotoisuutensa (nominative singular)
samanmuotoisuutensa (nominative plural)
samanmuotoisuutensa (accusative nominative singular)
samanmuotoisuutensa (accusative nominative plural)
samanmuotoisuutensa (accusative genitive singular)
samanmuotoisuutensa (accusative genitive plural)
samanmuotoisuutensa (genitive singular)
samanmuotoisuuksiensa (genitive plural)
samanmuotoisuuttaan (partitive singular)
samanmuotoisuuttansa (partitive singular)
samanmuotoisuuksiaan (partitive plural)
samanmuotoisuuksiansa (partitive plural)
samanmuotoisuudessaan (inessive singular)
samanmuotoisuudessansa (inessive singular)
samanmuotoisuuksissaan (inessive plural)
samanmuotoisuuksissansa (inessive plural)
samanmuotoisuudestaan (elative singular)
samanmuotoisuudestansa (elative singular)
samanmuotoisuuksistaan (elative plural)
samanmuotoisuuksistansa (elative plural)
samanmuotoisuuteensa (illative singular)
samanmuotoisuuksiinsa (illative plural)
samanmuotoisuudellaan (adessive singular)
samanmuotoisuudellansa (adessive singular)
samanmuotoisuuksillaan (adessive plural)
samanmuotoisuuksillansa (adessive plural)
samanmuotoisuudeltaan (ablative singular)
samanmuotoisuudeltansa (ablative singular)
samanmuotoisuuksiltaan (ablative plural)
samanmuotoisuuksiltansa (ablative plural)
samanmuotoisuudelleen (allative singular)
samanmuotoisuudellensa (allative singular)
samanmuotoisuuksilleen (allative plural)
samanmuotoisuuksillensa (allative plural)
samanmuotoisuutenaan (essive singular)
samanmuotoisuutenansa (essive singular)
samanmuotoisuuksinaan (essive plural)
samanmuotoisuuksinansa (essive plural)
samanmuotoisuudekseen (singular translative)
samanmuotoisuudeksensa (singular translative)
samanmuotoisuuksikseen (plural translative)
samanmuotoisuuksiksensa (plural translative)
samanmuotoisuudettaan (abessive singular)
samanmuotoisuudettansa (abessive singular)
samanmuotoisuuksittaan (abessive plural)
samanmuotoisuuksittansa (abessive plural)
samanmuotoisuuksineen (comitative plural)
samanmuotoisuuksinensa (comitative plural)

[ˈs̠ɑ̝mɑ̝mˌmuo̞̯t̪o̞i̯s̠uːs̠]


মান

man (romanization)
মান (indefinite nominative)
মান (indefinite objective)
মানকে  / manke (semantically definite)) (indefinite objective)
মানের (genitive indefinite)
মানে (indefinite locative)
মানটা (definite nominative singular)
মানগুলা (definite nominative plural)
মানগুলো , mangulo (formal)) (definite nominative plural)
মানটা (definite objective singular)
মানগুলা (definite objective plural)
মানগুলো , mangulo (formal)) (definite objective plural)
মানটার (definite genitive singular)
মানগুলার (definite genitive plural)
মানগুলোর , mangulor (formal)) (definite genitive plural)
মানটাতে (definite locative singular)
মানটায় (definite locative singular)
মানগুলাতে (definite locative plural)
মানগুলায় (definite locative plural)
Objective Note: In some dialects

bn-decl-noun

man (semantically general or indefinite) / manke (semantically definite)

মানটা , মানটি

মানগুলা, মানগুলো

মানটা, মানটি

মানগুলা, মানগুলো

মানটার, মানটির

মানগুলার, মানগুলোর

mangular (colloquial), mangulor (formal)

মানটাতে / মানটায়, মানটিতে

manṭate / manṭay (colloquial), manṭite (formal)

মানগুলাতে / মানগুলায়, মানগুলোতে

mangulate / mangulay (colloquial), mangulote (formal)

Borrowed from Sanskrit मान (māna, “measuring out, dimension”), from मा (mā, “to measure; to mete out”) + [Term?] (nominalization suffix), from Proto-Indo-European *meh₁-.


Clifford algebra

en-noun

Clifford algebra (plural Clifford algebras)

Named after William Kingdon Clifford (1845–1879), an English mathematician and philosopher.

(algebra, mathematical physics) A unital associative algebra which generalizes the algebra of quaternions but which is not necessarily a division algebra; it is generated by a set of γᵢ (with i ranging from, say, 1 to n) such that the square of each γᵢ is fixed to be either +1 or −1, depending on each i, and such that any product γᵢγⱼ anticommutes when its factors are distinct (i.e., when i ne j).

Clifford algebra
William Kingdon Clifford


homological algebra

The notion of chain complex is central to homological algebra.

The development of homological algebra was closely intertwined with the emergence of category theory.

Homological algebra for our purposes consists of studying certain abelian groups Hⁿ(G,A) and H#95;n(G,A), known as the nth cohomology and homology groups of the group G with coefficients in the G-module A.

2002, C. R. Leedham-Green, S. McKay, The Structure of Groups of Prime Power Order, Oxford University Press, page 171:

A similar shift of interpretation of CT took place at about the same time in another context, namely homological algebra.

2007, Ralph Krömer, Tool and Object: A History and Philosophy of Category Theory, Springer (Birkhäuser), page 93:

In Section 4.1, we shall introduce some minimal amount of homological algebra needed to launch singular homology.

2014, Anant R. Shastri, Basic Algebraic Topology, Taylor & Francis (CRC Press / Chapman & Hall), page 169:

(algebra) The branch of mathematics dealing with homology and in particular with homological functors and the algebraic structures they entail.


Witt group

Named after German mathematician Ernst Witt (1911–1991), who introduced the concept in 1937.

groupe de Witt

group of equivalence classes found within a field, variety or category

A general method of studying the Witt group of a smooth variety is through the graded group associated to the filtration induced by the filtration of the Witt group of the function field by powers of the fundamental ideal of even rank forms.

1995, Raman Parimala, “Study of quadratic forms - Some connections with geometry”, in S. D. Chatterji, editor, Proceedings of the International Congress of Mathematicians, Zürich m94, Birkhäuser, page 328:

2011, Marco Schlichting, Higher Algebraic K-theory, Guillermo Cortiñas (editor), Topics in Algebraic and Topological K-Theory, Springer, Lecture Notes in Mathematics 2008, page 167,
The second reason for this emphasis is that an analog of the Thomason-Waldhausen Localization Theorem also holds for many other (co-) homology theories besides K-theory, among which Hochschild homology, (negative, periodic, ordinary) cyclic homology [49], topological Hochschild (and cyclic) homology [2], triangular Witt groups [6] and higher Grothendieck–Witt groups [77].

The Witt group of a category with duality is given as the quotient of the isometry classes of symmetric spaces modulo metabolic spaces.[…]For coherent and derived Witt groups, the derived tensor product of complexes gives rise to duality-preserving functions and consequently to pairings in triangular Witt groups, cf. [GN03].

2020, Matthias Wendt, “Oriented Schubert calculus in Chow-Witt rings of Grassmannians”, in Federico Binda, Marc Levine, Manh Toan Nguyen, Oliver Röndigs, editors, Motivic Homotopy Theory and Refined Enumerative Geometry, American Mathematical Society, pages 239–240:

equivalence relation
equivalence relation

metabolic quadratic space
metabolic quadratic space

(algebra) Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;

Given a field k of characteristic ≠ 2, the abelian group of equivalence classes of nondegenerate symmetric bilinear forms over k (where the equivalence relation is such that two forms are equivalent if each is obtainable from the other by adding a metabolic quadratic space), with the group operation corresponding to that of orthogonal direct sum of forms;
(algebraic geometry, by extension) given a variety X, the quotient of the Grothendieck group of isometry classes of quadratic spaces on X, with respect to orthogonal sum, modulo the subgroup generated by metabolic spaces
(category theory, by extension) given a category with duality, the quotient of isometry classes of symmetric spaces, modulo metabolic spaces.


공변

Sino-Korean word from 共 (“together”) + 變 (“change”).

ko-etym-sino

(almost always compounded, algebra) covariant


kuadrat

From Dutch kwadraat, from Middle French quadrat, from Latin quadrātum.

Menurut hukum gravitasi universal Newton, tiap partikel memiliki gaya tarik menarik dengan partikel lain, yang berbanding lurus dengan perkalian massa kedua partikel dan berbanding terbalik dengan kuadrat jarak antara kedua partikel.

According to Newton's law of universal gravitation, every particle has an attracting force with another particle, that is directly proportional to the product of the masses of the two particles and inversely proportional to the square of the distance between the two particles.

(algebra) square; the product of a number or quantity multiplied by itself


kuadrat

Tiga kuadrat tambah empat kuadrat sama dengan lima kuadrat.

Three squared plus four squared equals five squared.

(algebra) squared; raised to the second power


անհայտ

anhayt (romanization)
անհայտ (nominative singular)
անհայտներ (nominative plural)
անհայտի (dative singular)
անհայտների (dative plural)
անհայտից (ablative singular)
անհայտներից (ablative plural)
անհայտով (instrumental singular)
անհայտներով (instrumental plural)
անհայտում (locative singular)
անհայտներում (locative plural)
անհայտը (definite nominative singular)
անհայտն (definite nominative singular)
անհայտները (definite nominative plural)
անհայտներն (definite nominative plural)
անհայտին (dative definite singular)
անհայտներին (dative definite plural)
անհայտս (first-person nominative possessive singular)
անհայտներս (first-person nominative plural possessive)
անհայտիս (dative first-person possessive singular)
անհայտներիս (dative first-person plural possessive)
անհայտիցս (ablative first-person possessive singular)
անհայտներիցս (ablative first-person plural possessive)
անհայտովս (first-person instrumental possessive singular)
անհայտներովս (first-person instrumental plural possessive)
անհայտումս (first-person locative possessive singular)
անհայտներումս (first-person locative plural possessive)
անհայտդ (nominative possessive second-person singular)
անհայտներդ (nominative plural possessive second-person)
անհայտիդ (dative possessive second-person singular)
անհայտներիդ (dative plural possessive second-person)
անհայտիցդ (ablative possessive second-person singular)
անհայտներիցդ (ablative plural possessive second-person)
անհայտովդ (instrumental possessive second-person singular)
անհայտներովդ (instrumental plural possessive second-person)
անհայտումդ (locative possessive second-person singular)
անհայտներումդ (locative plural possessive second-person)
անյայտ (alternative traditional)

hy-decl-noun

անհայտը / անհայտն

անհայտները / անհայտներն

անհայտներում

անհայտներիցս

անհայտներովս

անհայտներումս

անհայտներիցդ

անհայտներովդ

անհայտներումդ

From Old Armenian անյայտ (anyayt); by surface analysis, ան- (an-) + հայտ (hayt).


meçhul

From Ottoman Turkish مجهول (mechul), from Arabic مَجْهُول (majhūl).


ezezagun

ezezagun (absolutive indefinite)
ezezaguna (absolutive indefinite singular)
ezezagunak (absolutive indefinite plural)
ezezagunek (ergative indefinite)
ezezagunak (ergative indefinite singular)
ezezagunek (ergative indefinite plural)
ezezaguni (dative indefinite)
ezezagunari (dative indefinite singular)
ezezagunei (dative indefinite plural)
ezezagunen (genitive indefinite)
ezezagunaren (genitive indefinite singular)
ezezagunen (genitive indefinite plural)
ezezagunekin (comitative indefinite)
ezezagunarekin (comitative indefinite singular)
ezezagunekin (comitative indefinite plural)
ezezagunengatik (causative indefinite)
ezezagunarengatik (causative indefinite singular)
ezezagunengatik (causative indefinite plural)
ezezagunentzat (benefactive indefinite)
ezezagunarentzat (benefactive indefinite singular)
ezezagunentzat (benefactive indefinite plural)
ezezagunez (indefinite instrumental)
ezezagunaz (indefinite instrumental singular)
ezezagunez (indefinite instrumental plural)
ezezagunengan (indefinite inessive)
ezezagunarengan (indefinite inessive singular)
ezezagunengan (indefinite inessive plural)
ezezagunetan (indefinite inessive)
ezezagunean (indefinite inessive singular)
ezezagunetan (indefinite inessive plural)
ezezagunetako (indefinite locative)
ezezaguneko (indefinite locative singular)
ezezagunetako (indefinite locative plural)
ezezagunengana (allative indefinite)
ezezagunarengana (allative indefinite singular)
ezezagunengana (allative indefinite plural)
ezezagunetara (allative indefinite)
ezezagunera (allative indefinite singular)
ezezagunetara (allative indefinite plural)
ezezagunenganaino (indefinite terminative)
ezezagunarenganaino (indefinite singular terminative)
ezezagunenganaino (indefinite plural terminative)
ezezagunetaraino (indefinite terminative)
ezezaguneraino (indefinite singular terminative)
ezezagunetaraino (indefinite plural terminative)
ezezagunenganantz (directive indefinite)
ezezagunarenganantz (directive indefinite singular)
ezezagunenganantz (directive indefinite plural)
ezezagunetarantz (directive indefinite)
ezezagunerantz (directive indefinite singular)
ezezagunetarantz (directive indefinite plural)
ezezagunenganako (destinative indefinite)
ezezagunarenganako (destinative indefinite singular)
ezezagunenganako (destinative indefinite plural)
ezezagunetarako (destinative indefinite)
ezezagunerako (destinative indefinite singular)
ezezagunetarako (destinative indefinite plural)
ezezagunengandik (ablative indefinite)
ezezagunarengandik (ablative indefinite singular)
ezezagunengandik (ablative indefinite plural)
ezezagunetatik (ablative indefinite)
ezezagunetik (ablative indefinite singular)
ezezagunetatik (ablative indefinite plural)
ezezagunik (indefinite partitive)
ezezaguntzat (indefinite prolative)

(inanimate, algebra) unknown (variable whose value is to be found)


增根

/t͡sɤŋ⁵⁵ kən⁵⁵/

/t͡sɤŋ⁵⁵ kən⁵⁵/


daimi kəmiyyət

az-noun

daimi kəmiyyət (definite accusative daimi kəmiyyəti, plural daimi kəmiyyətlər)

daimi kəmiyyəti (accusative definite)
daimi kəmiyyətlər (plural)
daimi kəmiyyət (nominative singular)
daimi kəmiyyətlər (nominative plural)
daimi kəmiyyəti (accusative definite singular)
daimi kəmiyyətləri (accusative definite plural)
daimi kəmiyyətə (dative singular)
daimi kəmiyyətlərə (dative plural)
daimi kəmiyyətdə (locative singular)
daimi kəmiyyətlərdə (locative plural)
daimi kəmiyyətdən (ablative singular)
daimi kəmiyyətlərdən (ablative plural)
daimi kəmiyyətin (definite genitive singular)
daimi kəmiyyətlərin (definite genitive plural)
daimi kəmiyyətim (first-person nominative possessive singular)
daimi kəmiyyətlərim (first-person nominative possessive singular)
daimi kəmiyyətin (nominative possessive second-person singular)
daimi kəmiyyətlərin (nominative possessive second-person singular)
daimi kəmiyyəti (nominative possessive singular third-person)
daimi kəmiyyətləri (nominative possessive singular third-person)
daimi kəmiyyətimiz (first-person nominative plural possessive)
daimi kəmiyyətlərimiz (first-person nominative plural possessive)
daimi kəmiyyətiniz (nominative plural possessive second-person)
daimi kəmiyyətləriniz (nominative plural possessive second-person)
daimi kəmiyyəti (nominative plural possessive third-person)
daimi kəmiyyətləri (nominative plural possessive third-person)
daimi kəmiyyətimi (accusative first-person possessive singular)
daimi kəmiyyətlərimi (accusative first-person possessive singular)
daimi kəmiyyətini (accusative possessive second-person singular)
daimi kəmiyyətlərini (accusative possessive second-person singular)
daimi kəmiyyətini (accusative possessive singular third-person)
daimi kəmiyyətlərini (accusative possessive singular third-person)
daimi kəmiyyətimizi (accusative first-person plural possessive)
daimi kəmiyyətlərimizi (accusative first-person plural possessive)
daimi kəmiyyətinizi (accusative plural possessive second-person)
daimi kəmiyyətlərinizi (accusative plural possessive second-person)
daimi kəmiyyətini (accusative plural possessive third-person)
daimi kəmiyyətlərini (accusative plural possessive third-person)
daimi kəmiyyətimə (dative first-person possessive singular)
daimi kəmiyyətlərimə (dative first-person possessive singular)
daimi kəmiyyətinə (dative possessive second-person singular)
daimi kəmiyyətlərinə (dative possessive second-person singular)
daimi kəmiyyətinə (dative possessive singular third-person)
daimi kəmiyyətlərinə (dative possessive singular third-person)
daimi kəmiyyətimizə (dative first-person plural possessive)
daimi kəmiyyətlərimizə (dative first-person plural possessive)
daimi kəmiyyətinizə (dative plural possessive second-person)
daimi kəmiyyətlərinizə (dative plural possessive second-person)
daimi kəmiyyətinə (dative plural possessive third-person)
daimi kəmiyyətlərinə (dative plural possessive third-person)
daimi kəmiyyətimdə (first-person locative possessive singular)
daimi kəmiyyətlərimdə (first-person locative possessive singular)
daimi kəmiyyətində (locative possessive second-person singular)
daimi kəmiyyətlərində (locative possessive second-person singular)
daimi kəmiyyətində (locative possessive singular third-person)
daimi kəmiyyətlərində (locative possessive singular third-person)
daimi kəmiyyətimizdə (first-person locative plural possessive)
daimi kəmiyyətlərimizdə (first-person locative plural possessive)
daimi kəmiyyətinizdə (locative plural possessive second-person)
daimi kəmiyyətlərinizdə (locative plural possessive second-person)
daimi kəmiyyətində (locative plural possessive third-person)
daimi kəmiyyətlərində (locative plural possessive third-person)
daimi kəmiyyətimdən (ablative first-person possessive singular)
daimi kəmiyyətlərimdən (ablative first-person possessive singular)
daimi kəmiyyətindən (ablative possessive second-person singular)
daimi kəmiyyətlərindən (ablative possessive second-person singular)
daimi kəmiyyətindən (ablative possessive singular third-person)
daimi kəmiyyətlərindən (ablative possessive singular third-person)
daimi kəmiyyətimizdən (ablative first-person plural possessive)
daimi kəmiyyətlərimizdən (ablative first-person plural possessive)
daimi kəmiyyətinizdən (ablative plural possessive second-person)
daimi kəmiyyətlərinizdən (ablative plural possessive second-person)
daimi kəmiyyətindən (ablative plural possessive third-person)
daimi kəmiyyətlərindən (ablative plural possessive third-person)
daimi kəmiyyətimin (first-person genitive possessive singular)
daimi kəmiyyətlərimin (first-person genitive possessive singular)
daimi kəmiyyətinin (genitive possessive second-person singular)
daimi kəmiyyətlərinin (genitive possessive second-person singular)
daimi kəmiyyətinin (genitive possessive singular third-person)
daimi kəmiyyətlərinin (genitive possessive singular third-person)
daimi kəmiyyətimizin (first-person genitive plural possessive)
daimi kəmiyyətlərimizin (first-person genitive plural possessive)
daimi kəmiyyətinizin (genitive plural possessive second-person)
daimi kəmiyyətlərinizin (genitive plural possessive second-person)
daimi kəmiyyətinin (genitive plural possessive third-person)
daimi kəmiyyətlərinin (genitive plural possessive third-person)

LL-Q9292 (aze)-Azerbaijani audiorecordings-daimi kəmiyyət.wav

(algebra) constant (quantity that remains at a fixed value throughout a given discussion)


abelsk gruppe

head

abelsk gruppe f or m (definite singular abelske gruppa or abelske gruppen, indefinite plural abelske grupper, definite plural abelske gruppene)

abelske gruppa (definite singular)
abelske gruppen (definite singular)
abelske grupper (indefinite plural)
abelske gruppene (definite plural)

abelsk + gruppe, first part from the last name of Norwegian mathematician Niels Henrik Abel, + the prefix -sk (“-ish”), from Proto-Germanic *-iskaz, from Proto-Indo-European *-iskos. Last part from German Gruppe (“group”), from French groupe (“group”), from Italian gruppo (“group, cluster, party”), from Vulgar Latin *cruppo, Renaissance Latin grupus (“group”), from Proto-Germanic *kruppaz (“lump, round mass, body, crop”), from Proto-Indo-European *grewb- (“to crumple, bend, crawl”), from Proto-Indo-European *ger- (“to turn, wind”).

der

(algebra, mathematics) an abelian group (a group in which the group operation is commutative)


вынести за скобки

ru-verb

вы́нести за ско́бки

выноси́ть за ско́бки

вы́нести за ско́бки • (výnesti za skóbki) pf (imperfective выноси́ть за ско́бки)

вы́нести за ско́бки (canonical)
výnesti za skóbki (romanization)
выноси́ть за ско́бки (imperfective)

[ˈvɨnʲɪsʲtʲɪ zɐ‿ˈskopkʲɪ]

Literally, “to take something out of the parentheses”.

lit

(transitive, algebra) to factor out (to isolate a common factor from an expression)


移項

/i³⁵ ɕi̯ɑŋ⁵¹/

/jiː²¹ hɔːŋ²²/

/i³⁵ ɕi̯ɑŋ⁵¹/

/jiː²¹ hɔːŋ²²/

(intransitive, algebra) to transpose terms


布爾函數

ㄅㄨˋ ㄦˇ ㄏㄢˊ ㄕㄨˋ

ㄅㄨˋ ㄦˇ ㄏㄢˊ ㄕㄨˋ

/pu⁵¹ ˀɤɻ²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

/pu⁵¹ ˀɤɻ²¹⁴⁻²¹ xän³⁵ ʂu⁵¹/

(algebra, logic, computing) Boolean function


torsion subgroup

en-noun

torsion subgroup (plural torsion subgroups)

A standard theorem about finitely generated abelian groups tells us that E(#92;mathbb#123;Q#125;) looks like
#92;qquadE(#92;mathbb#123;Q#125;)#92;cong(#92;mbox#123;FiniteGroup#125;)#92;times#92;underbrace#123;#92;mathbb#123;Z#125;#92;times#92;mathbb#123;Z#125;#92;times...#92;times#92;mathbb#123;Z

2006 July 7, Joseph H. Silverman, An Introduction to the Theory of Elliptic Curves:

(algebra) Subgroup of an abelian group whose generators have finite order.


餘式定理

ㄩˊ ㄕˋ ㄉㄧㄥˋ ㄌㄧˇ

ㄩˊ ㄕˋ ㄉㄧㄥˋ ㄌㄧˇ

/y³⁵ ʂʐ̩⁵¹⁻⁵³ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

/jyː²¹ sɪk̚⁵ tɪŋ²² lei̯¹³/

/y³⁵ ʂʐ̩⁵¹⁻⁵³ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

/jyː²¹ sɪk̚⁵ tɪŋ²² lei̯¹³/

(algebra) polynomial remainder theorem; remainder theorem


因式定理

ㄧㄣ ㄕˋ ㄉㄧㄥˋ ㄌㄧˇ

ㄧㄣ ㄕˋ ㄉㄧㄥˋ ㄌㄧˇ

/in⁵⁵ ʂʐ̩⁵¹⁻⁵³ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

/jɐn⁵⁵ sɪk̚⁵ tɪŋ²² lei̯¹³/

/in⁵⁵ ʂʐ̩⁵¹⁻⁵³ tiŋ⁵¹ li²¹⁴⁻²¹⁽⁴⁾/

/jɐn⁵⁵ sɪk̚⁵ tɪŋ²² lei̯¹³/


単項式

単項式 (canonical)
tankōshiki (romanization)


ബീജഗണിതം

head

ബീജഗണിതം • (bījagaṇitaṁ)

/biːd͡ʒɐɡɐɳid̪ɐm/

Borrowed from Sanskrit बीजगणित (bījagaṇita).


necunoscută

necunoscute (plural)
necunoscută (accusative indefinite nominative singular)
necunoscuta (accusative definite nominative singular)
necunoscute (accusative indefinite nominative plural)
necunoscutele (accusative definite nominative plural)
necunoscute (indefinite singular)
necunoscutei (definite singular)
necunoscute (indefinite plural)
necunoscutelor (definite plural)
necunoscută (singular vocative)
necunoscuto (singular vocative)
necunoscutelor (plural vocative)


monómio

monómios (plural)
monômio (alternative Brazil)

(algebra) monomial (polynomial with one terms)


konfigurasi

From Dutch configuratie, from Latin cōnfigūrātiō.

(algebra) a finite set of points and lines (and sometimes planes), generally with equal numbers of points per line and equal numbers of lines per point


數域

/ʂu⁵¹⁻⁵³ y⁵¹/

/ʂu⁵¹⁻⁵³ y⁵¹/


asocjatywny

pl-adj

asocjatywny (not comparable, no derived adverb)

asocjatywny (masculine nominative singular)
asocjatywna (feminine nominative singular)
asocjatywne (neuter nominative singular)
asocjatywni (nominative plural virile)
asocjatywne (nominative plural)
asocjatywnego (genitive masculine singular)
asocjatywnej (feminine genitive singular)
asocjatywnego (genitive neuter singular)
asocjatywnych (genitive plural)
asocjatywnych (genitive plural virile)
asocjatywnemu (dative masculine singular)
asocjatywnej (dative feminine singular)
asocjatywnemu (dative neuter singular)
asocjatywnym (dative plural)
asocjatywnym (dative plural virile)
asocjatywnego (accusative animate masculine singular)
asocjatywny (accusative inanimate masculine singular)
asocjatywną (accusative feminine singular)
asocjatywne (accusative neuter singular)
asocjatywnych (accusative plural virile)
asocjatywne (accusative plural)
asocjatywnym (instrumental masculine singular)
asocjatywną (feminine instrumental singular)
asocjatywnym (instrumental neuter singular)
asocjatywnymi (instrumental plural)
asocjatywnymi (instrumental plural virile)
asocjatywnym (locative masculine singular)
asocjatywnej (feminine locative singular)
asocjatywnym (locative neuter singular)
asocjatywnych (locative plural)
asocjatywnych (locative plural virile)

Adapted borrowing of French associatif + -ny. First attested in 1906.


asocjatywność

asocjatywność (nominative singular)
asocjatywności (genitive singular)
asocjatywności (dative singular)
asocjatywność (accusative singular)
asocjatywnością (instrumental singular)
asocjatywności (locative singular)
asocjatywności (singular vocative)


hyperbolic quaternion

en-noun

hyperbolic quaternion (plural hyperbolic quaternions)

(mathematics, abstract algebra) A nonassociative algebra over the real numbers with elements of the form: q = a + bi + cj + dk, a,b,c,d {R}


тэҥнэбил

head

тэҥнэбил • (teñnebil)

sah-noun

тэҥнэбил • (teñnebil)

икки биллибэттээх тэҥнэбил

тэҥнэбил w:sah:тэҥнэбил


биллибэт

икки биллибэттээх тэҥнэбил


ബഹുപദം

Borrowed from Sanskrit बहुपद (bahupada); Cognate with Hindi बहुपद (bahupad).


podstawić

podstawiać (imperfective)
podstawić (infinitive)
podstawię (future singular)
podstawimy (future plural)
podstawisz (future singular)
podstawicie (future plural)
podstawi (future singular third-person)
podstawią (future plural third-person)
podstawi się (future impersonal)
podstawiłem (masculine past singular)
-(e)m podstawił (masculine past singular)
podstawiłam (feminine past singular)
-(e)m podstawiła (feminine past singular)
podstawiłom (neuter past singular)
-(e)m podstawiło (neuter past singular)
podstawiliśmy (past plural virile)
-(e)śmy podstawili (past plural virile)
podstawiłyśmy (nonvirile past plural)
-(e)śmy podstawiły (nonvirile past plural)
podstawiłeś (masculine past singular)
-(e)ś podstawił (masculine past singular)
podstawiłaś (feminine past singular)
-(e)ś podstawiła (feminine past singular)
podstawiłoś (neuter past singular)
-(e)ś podstawiło (neuter past singular)
podstawiliście (past plural virile)
-(e)ście podstawili (past plural virile)
podstawiłyście (nonvirile past plural)
-(e)ście podstawiły (nonvirile past plural)
podstawił (masculine past singular third-person)
podstawiła (feminine past singular third-person)
podstawiło (neuter past singular third-person)
podstawili (past plural third-person virile)
podstawiły (nonvirile past plural third-person)
podstawiono (impersonal past)
podstawiłbym (conditional masculine singular)
bym podstawił (conditional masculine singular)
podstawiłabym (conditional feminine singular)
bym podstawiła (conditional feminine singular)
podstawiłobym (conditional neuter singular)
bym podstawiło (conditional neuter singular)
podstawilibyśmy (conditional plural virile)
byśmy podstawili (conditional plural virile)
podstawiłybyśmy (conditional nonvirile plural)
byśmy podstawiły (conditional nonvirile plural)
podstawiłbyś (conditional masculine singular)
byś podstawił (conditional masculine singular)
podstawiłabyś (conditional feminine singular)
byś podstawiła (conditional feminine singular)
podstawiłobyś (conditional neuter singular)
byś podstawiło (conditional neuter singular)
podstawilibyście (conditional plural virile)
byście podstawili (conditional plural virile)
podstawiłybyście (conditional nonvirile plural)
byście podstawiły (conditional nonvirile plural)
podstawiłby (conditional masculine singular third-person)
by podstawił (conditional masculine singular third-person)
podstawiłaby (conditional feminine singular third-person)
by podstawiła (conditional feminine singular third-person)
podstawiłoby (conditional neuter singular third-person)
by podstawiło (conditional neuter singular third-person)
podstawiliby (conditional plural third-person virile)
by podstawili (conditional plural third-person virile)
podstawiłyby (conditional nonvirile plural third-person)
by podstawiły (conditional nonvirile plural third-person)
podstawiono by (conditional impersonal)
niech podstawię (imperative singular)
podstawmy (imperative plural)
podstaw (imperative singular)
podstawcie (imperative plural)
niech podstawi (imperative singular third-person)
niech podstawią (imperative plural third-person)
podstawiony (adjectival masculine participle passive singular)
podstawiona (adjectival feminine participle passive singular)
podstawione (adjectival neuter participle passive singular)
podstawieni (adjectival participle passive plural virile)
podstawione (adjectival nonvirile participle passive plural)
podstawiwszy (adverbial anterior participle)
podstawienie (noun-from-verb)

(transitive, reflexive with się, algebra, chemistry) to substitute


podstawiać

podstawić (imperfective)
podstawiać (infinitive)
podstawiam (present singular)
podstawiamy (plural present)
podstawiasz (present singular)
podstawiacie (plural present)
podstawia (present singular third-person)
podstawiają (plural present third-person)
podstawia się (impersonal present)
podstawiałem (masculine past singular)
-(e)m podstawiał (masculine past singular)
podstawiałam (feminine past singular)
-(e)m podstawiała (feminine past singular)
podstawiałom (neuter past singular)
-(e)m podstawiało (neuter past singular)
podstawialiśmy (past plural virile)
-(e)śmy podstawiali (past plural virile)
podstawiałyśmy (nonvirile past plural)
-(e)śmy podstawiały (nonvirile past plural)
podstawiałeś (masculine past singular)
-(e)ś podstawiał (masculine past singular)
podstawiałaś (feminine past singular)
-(e)ś podstawiała (feminine past singular)
podstawiałoś (neuter past singular)
-(e)ś podstawiało (neuter past singular)
podstawialiście (past plural virile)
-(e)ście podstawiali (past plural virile)
podstawiałyście (nonvirile past plural)
-(e)ście podstawiały (nonvirile past plural)
podstawiał (masculine past singular third-person)
podstawiała (feminine past singular third-person)
podstawiało (neuter past singular third-person)
podstawiali (past plural third-person virile)
podstawiały (nonvirile past plural third-person)
podstawiano (impersonal past)
będę podstawiał (future masculine singular)
będę podstawiać (future masculine singular)
będę podstawiała (feminine future singular)
będę podstawiać (feminine future singular)
będę podstawiało (future neuter singular)
będę podstawiać (future neuter singular)
będziemy podstawiali (future plural virile)
będziemy podstawiać (future plural virile)
będziemy podstawiały (future nonvirile plural)
będziemy podstawiać (future nonvirile plural)
będziesz podstawiał (future masculine singular)
będziesz podstawiać (future masculine singular)
będziesz podstawiała (feminine future singular)
będziesz podstawiać (feminine future singular)
będziesz podstawiało (future neuter singular)
będziesz podstawiać (future neuter singular)
będziecie podstawiali (future plural virile)
będziecie podstawiać (future plural virile)
będziecie podstawiały (future nonvirile plural)
będziecie podstawiać (future nonvirile plural)
będzie podstawiał (future masculine singular third-person)
będzie podstawiać (future masculine singular third-person)
będzie podstawiała (feminine future singular third-person)
będzie podstawiać (feminine future singular third-person)
będzie podstawiało (future neuter singular third-person)
będzie podstawiać (future neuter singular third-person)
będą podstawiali (future plural third-person virile)
będą podstawiać (future plural third-person virile)
będą podstawiały (future nonvirile plural third-person)
będą podstawiać (future nonvirile plural third-person)
będzie podstawiać się (future impersonal)
podstawiałbym (conditional masculine singular)
bym podstawiał (conditional masculine singular)
podstawiałabym (conditional feminine singular)
bym podstawiała (conditional feminine singular)
podstawiałobym (conditional neuter singular)
bym podstawiało (conditional neuter singular)
podstawialibyśmy (conditional plural virile)
byśmy podstawiali (conditional plural virile)
podstawiałybyśmy (conditional nonvirile plural)
byśmy podstawiały (conditional nonvirile plural)
podstawiałbyś (conditional masculine singular)
byś podstawiał (conditional masculine singular)
podstawiałabyś (conditional feminine singular)
byś podstawiała (conditional feminine singular)
podstawiałobyś (conditional neuter singular)
byś podstawiało (conditional neuter singular)
podstawialibyście (conditional plural virile)
byście podstawiali (conditional plural virile)
podstawiałybyście (conditional nonvirile plural)
byście podstawiały (conditional nonvirile plural)
podstawiałby (conditional masculine singular third-person)
by podstawiał (conditional masculine singular third-person)
podstawiałaby (conditional feminine singular third-person)
by podstawiała (conditional feminine singular third-person)
podstawiałoby (conditional neuter singular third-person)
by podstawiało (conditional neuter singular third-person)
podstawialiby (conditional plural third-person virile)
by podstawiali (conditional plural third-person virile)
podstawiałyby (conditional nonvirile plural third-person)
by podstawiały (conditional nonvirile plural third-person)
podstawiano by (conditional impersonal)
niech podstawiam (imperative singular)
podstawiajmy (imperative plural)
podstawiaj (imperative singular)
podstawiajcie (imperative plural)
niech podstawia (imperative singular third-person)
niech podstawiają (imperative plural third-person)
podstawiający (active adjectival masculine participle singular)
podstawiająca (active adjectival feminine participle singular)
podstawiające (active adjectival neuter participle singular)
podstawiający (active adjectival participle plural virile)
podstawiające (active adjectival nonvirile participle plural)
podstawiany (adjectival masculine participle passive singular)
podstawiana (adjectival feminine participle passive singular)
podstawiane (adjectival neuter participle passive singular)
podstawiani (adjectival participle passive plural virile)
podstawiane (adjectival nonvirile participle passive plural)
podstawiając (adjectival contemporary participle)
podstawianie (noun-from-verb)


外代數

/waɪ̯⁵¹⁻⁵³ taɪ̯⁵¹⁻⁵³ ʂu⁵¹/

/waɪ̯⁵¹⁻⁵³ taɪ̯⁵¹⁻⁵³ ʂu⁵¹/


rational root theorem

The rational root theorem states that if the rational number p#47;q is a root of the polynomial equation a#95;nxⁿ#43;a#95;#123;n-1#125;x#123;n-1#125;#43;#92;cdots#43;a#95;0#61;0, with a#95;0,#92;ldotsa#95;n#92;in#92;mathbb#123;Z#125;, then p#92;verta#95;0 and q#92;verta#95;n.

is irreducible over Q [x].

2015, Marlow Anderson, Todd Feil, A First Course in Abstract Algebra, Taylor & Francis (CRC Press), 3rd Edition, page 50, Use the Rational Root Theorem 5.6 to argue that x³+x+7

We demonstrate how to use the rational root theorem to prove the irrationality of many numbers.

2017, Martin H. Weissman, An Illustrated Theory of Numbers, American Mathematical Society, page 84:

The rational root theorem has you create a list of possible rational roots using the lead coefficient and constant in the polynomial equation.

2018, Mary Jane Sterling, Pre-Calculus For Dummies, Wiley, page 85:

(algebra) A theorem which states a constraint on rational solutions of a polynomial equation with integer coefficients.


ពហុធា

km-noun

ពហុធា • (pĕəʼhuthiə)


eigensection

(algebra) A homogenous section whose associated Eulerian family diagonalizes a given element of a Lie algebra.


Bring radical

Named after Swedish mathematician Erland Samuel Bring (1736–1798).

named-after

(algebra) Synonym of ultraradical (“root of the polynomial x⁵ + x + a, where a is a complex number”).


incògnita

(algebra) unknown (variable whose value is to be found)


Cartesian equation

en-noun

Cartesian equation (plural Cartesian equations)

(geometry, algebra) An equation that describes a line or plane in terms of the relationship between the coordinates on the axes involved.


Auslander-Reiten theory

Introduced by Maurice Auslander and Idun Reiten (1975).

representation theory
representation theory

Auslander-Reiten sequence
Auslander-Reiten sequence

almost split sequence
almost split sequence

Auslander-Reiten quiver
Auslander-Reiten quiver

(algebra) The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers.


almost split sequence

almost split sequence (plural almost split sequences)

Auslander-Reiten sequence
Auslander-Reiten sequence#English

(algebra) Synonym of Auslander-Reiten sequence.


aljabar linier

id-noun

aljabar linier (plural aljabar-aljabar linier)


aljabar linear

aljabar linear (plural aljabar-aljabar linear)


אסוציאטיבי

he-adj

אָסוֹצְיָאטִיבִי

אָסוֹצְיָאטִיבִי • (asotsyativí)

אָסוֹצְיָאטִיבִי (canonical)
asotsyativí (romanization)


Monoid

de-noun

Monoid n (strong, genitive Monoides or Monoids, plural Monoide)

Monoides (genitive)
Monoids (genitive)
Monoide (plural)
Monoid (nominative singular)
Monoide (definite nominative plural)
Monoides (genitive singular)
Monoids (genitive singular)
Monoide (definite genitive plural)
Monoid (dative singular)
Monoide (dative singular)
Monoiden (dative definite plural)
Monoid (accusative singular)
Monoide (accusative definite plural)


corps commutatif

fr-noun

corps commutatif m (plural corps commutatifs)


supistettu porrasmuoto

supistettu porrasmuoto (nominative singular)
supistetut porrasmuodot (nominative plural)
supistettu porrasmuoto (accusative nominative singular)
supistetut porrasmuodot (accusative nominative plural)
supistetun porrasmuodon (accusative genitive singular)
supistetut porrasmuodot (accusative genitive plural)
supistetun porrasmuodon (genitive singular)
supistettujen porrasmuotojen (genitive plural)
supistettua porrasmuotoa (partitive singular)
supistettuja porrasmuotoja (partitive plural)
supistetussa porrasmuodossa (inessive singular)
supistetuissa porrasmuodoissa (inessive plural)
supistetusta porrasmuodosta (elative singular)
supistetuista porrasmuodoista (elative plural)
supistettuun porrasmuotoon (illative singular)
supistettuihin porrasmuotoihin (illative plural)
supistetulla porrasmuodolla (adessive singular)
supistetuilla porrasmuodoilla (adessive plural)
supistetulta porrasmuodolta (ablative singular)
supistetuilta porrasmuodoilta (ablative plural)
supistetulle porrasmuodolle (allative singular)
supistetuille porrasmuodoille (allative plural)
supistettuna porrasmuotona (essive singular)
supistettuina porrasmuotoina (essive plural)
supistetuksi porrasmuodoksi (singular translative)
supistetuiksi porrasmuodoiksi (plural translative)
supistetutta porrasmuodotta (abessive singular)
supistetuitta porrasmuodoitta (abessive plural)
supistetuin porrasmuodoin (instructive plural)
See the possessive forms below. (comitative)
supistettuni porrasmuotoni (nominative singular)
supistettuni porrasmuotoni (nominative plural)
supistettuni porrasmuotoni (accusative nominative singular)
supistettuni porrasmuotoni (accusative nominative plural)
supistettuni porrasmuotoni (accusative genitive singular)
supistettuni porrasmuotoni (accusative genitive plural)
supistettuni porrasmuotoni (genitive singular)
supistettujeni porrasmuotojeni (genitive plural)
supistettuani porrasmuotoani (partitive singular)
supistettujani porrasmuotojani (partitive plural)
supistetussani porrasmuodossani (inessive singular)
supistetuissani porrasmuodoissani (inessive plural)
supistetustani porrasmuodostani (elative singular)
supistetuistani porrasmuodoistani (elative plural)
supistettuuni porrasmuotooni (illative singular)
supistettuihini porrasmuotoihini (illative plural)
supistetullani porrasmuodollani (adessive singular)
supistetuillani porrasmuodoillani (adessive plural)
supistetultani porrasmuodoltani (ablative singular)
supistetuiltani porrasmuodoiltani (ablative plural)
supistetulleni porrasmuodolleni (allative singular)
supistetuilleni porrasmuodoilleni (allative plural)
supistettunani porrasmuotonani (essive singular)
supistettuinani porrasmuotoinani (essive plural)
supistetukseni porrasmuodokseni (singular translative)
supistetuikseni porrasmuodoikseni (plural translative)
supistetuttani porrasmuodottani (abessive singular)
supistetuittani porrasmuodoittani (abessive plural)
supistettuineni porrasmuotoineni (comitative plural)
supistettusi porrasmuotosi (nominative singular)
supistettusi porrasmuotosi (nominative plural)
supistettusi porrasmuotosi (accusative nominative singular)
supistettusi porrasmuotosi (accusative nominative plural)
supistettusi porrasmuotosi (accusative genitive singular)
supistettusi porrasmuotosi (accusative genitive plural)
supistettusi porrasmuotosi (genitive singular)
supistettujesi porrasmuotojesi (genitive plural)
supistettuasi porrasmuotoasi (partitive singular)
supistettujasi porrasmuotojasi (partitive plural)
supistetussasi porrasmuodossasi (inessive singular)
supistetuissasi porrasmuodoissasi (inessive plural)
supistetustasi porrasmuodostasi (elative singular)
supistetuistasi porrasmuodoistasi (elative plural)
supistettuusi porrasmuotoosi (illative singular)
supistettuihisi porrasmuotoihisi (illative plural)
supistetullasi porrasmuodollasi (adessive singular)
supistetuillasi porrasmuodoillasi (adessive plural)
supistetultasi porrasmuodoltasi (ablative singular)
supistetuiltasi porrasmuodoiltasi (ablative plural)
supistetullesi porrasmuodollesi (allative singular)
supistetuillesi porrasmuodoillesi (allative plural)
supistettunasi porrasmuotonasi (essive singular)
supistettuinasi porrasmuotoinasi (essive plural)
supistetuksesi porrasmuodoksesi (singular translative)
supistetuiksesi porrasmuodoiksesi (plural translative)
supistetuttasi porrasmuodottasi (abessive singular)
supistetuittasi porrasmuodoittasi (abessive plural)
supistettuinesi porrasmuotoinesi (comitative plural)
supistettumme porrasmuotomme (nominative singular)
supistettumme porrasmuotomme (nominative plural)
supistettumme porrasmuotomme (accusative nominative singular)
supistettumme porrasmuotomme (accusative nominative plural)
supistettumme porrasmuotomme (accusative genitive singular)
supistettumme porrasmuotomme (accusative genitive plural)
supistettumme porrasmuotomme (genitive singular)
supistettujemme porrasmuotojemme (genitive plural)
supistettuamme porrasmuotoamme (partitive singular)
supistettujamme porrasmuotojamme (partitive plural)
supistetussamme porrasmuodossamme (inessive singular)
supistetuissamme porrasmuodoissamme (inessive plural)
supistetustamme porrasmuodostamme (elative singular)
supistetuistamme porrasmuodoistamme (elative plural)
supistettuumme porrasmuotoomme (illative singular)
supistettuihimme porrasmuotoihimme (illative plural)
supistetullamme porrasmuodollamme (adessive singular)
supistetuillamme porrasmuodoillamme (adessive plural)
supistetultamme porrasmuodoltamme (ablative singular)
supistetuiltamme porrasmuodoiltamme (ablative plural)
supistetullemme porrasmuodollemme (allative singular)
supistetuillemme porrasmuodoillemme (allative plural)
supistettunamme porrasmuotonamme (essive singular)
supistettuinamme porrasmuotoinamme (essive plural)
supistetuksemme porrasmuodoksemme (singular translative)
supistetuiksemme porrasmuodoiksemme (plural translative)
supistetuttamme porrasmuodottamme (abessive singular)
supistetuittamme porrasmuodoittamme (abessive plural)
supistettuinemme porrasmuotoinemme (comitative plural)
supistettunne porrasmuotonne (nominative singular)
supistettunne porrasmuotonne (nominative plural)
supistettunne porrasmuotonne (accusative nominative singular)
supistettunne porrasmuotonne (accusative nominative plural)
supistettunne porrasmuotonne (accusative genitive singular)
supistettunne porrasmuotonne (accusative genitive plural)
supistettunne porrasmuotonne (genitive singular)
supistettujenne porrasmuotojenne (genitive plural)
supistettuanne porrasmuotoanne (partitive singular)
supistettujanne porrasmuotojanne (partitive plural)
supistetussanne porrasmuodossanne (inessive singular)
supistetuissanne porrasmuodoissanne (inessive plural)
supistetustanne porrasmuodostanne (elative singular)
supistetuistanne porrasmuodoistanne (elative plural)
supistettuunne porrasmuotoonne (illative singular)
supistettuihinne porrasmuotoihinne (illative plural)
supistetullanne porrasmuodollanne (adessive singular)
supistetuillanne porrasmuodoillanne (adessive plural)
supistetultanne porrasmuodoltanne (ablative singular)
supistetuiltanne porrasmuodoiltanne (ablative plural)
supistetullenne porrasmuodollenne (allative singular)
supistetuillenne porrasmuodoillenne (allative plural)
supistettunanne porrasmuotonanne (essive singular)
supistettuinanne porrasmuotoinanne (essive plural)
supistetuksenne porrasmuodoksenne (singular translative)
supistetuiksenne porrasmuodoiksenne (plural translative)
supistetuttanne porrasmuodottanne (abessive singular)
supistetuittanne porrasmuodoittanne (abessive plural)
supistettuinenne porrasmuotoinenne (comitative plural)
supistettunsa porrasmuotonsa (nominative singular)
supistettunsa porrasmuotonsa (nominative plural)
supistettunsa porrasmuotonsa (accusative nominative singular)
supistettunsa porrasmuotonsa (accusative nominative plural)
supistettunsa porrasmuotonsa (accusative genitive singular)
supistettunsa porrasmuotonsa (accusative genitive plural)
supistettunsa porrasmuotonsa (genitive singular)
supistettujensa porrasmuotojensa (genitive plural)
supistettuaan porrasmuotoaan (partitive singular)
supistettuaan porrasmuotoansa (partitive singular)
supistettuansa porrasmuotoaan (partitive singular)
supistettuansa porrasmuotoansa (partitive singular)
supistettujaan porrasmuotojaan (partitive plural)
supistettujaan porrasmuotojansa (partitive plural)
supistettujansa porrasmuotojaan (partitive plural)
supistettujansa porrasmuotojansa (partitive plural)
supistetussaan porrasmuodossaan (inessive singular)
supistetussaan porrasmuodossansa (inessive singular)
supistetussansa porrasmuodossaan (inessive singular)
supistetussansa porrasmuodossansa (inessive singular)
supistetuissaan porrasmuodoissaan (inessive plural)
supistetuissaan porrasmuodoissansa (inessive plural)
supistetuissansa porrasmuodoissaan (inessive plural)
supistetuissansa porrasmuodoissansa (inessive plural)
supistetustaan porrasmuodostaan (elative singular)
supistetustaan porrasmuodostansa (elative singular)
supistetustansa porrasmuodostaan (elative singular)
supistetustansa porrasmuodostansa (elative singular)
supistetuistaan porrasmuodoistaan (elative plural)
supistetuistaan porrasmuodoistansa (elative plural)
supistetuistansa porrasmuodoistaan (elative plural)
supistetuistansa porrasmuodoistansa (elative plural)
supistettuunsa porrasmuotoonsa (illative singular)
supistettuihinsa porrasmuotoihinsa (illative plural)
supistetullaan porrasmuodollaan (adessive singular)
supistetullaan porrasmuodollansa (adessive singular)
supistetullansa porrasmuodollaan (adessive singular)
supistetullansa porrasmuodollansa (adessive singular)
supistetuillaan porrasmuodoillaan (adessive plural)
supistetuillaan porrasmuodoillansa (adessive plural)
supistetuillansa porrasmuodoillaan (adessive plural)
supistetuillansa porrasmuodoillansa (adessive plural)
supistetultaan porrasmuodoltaan (ablative singular)
supistetultaan porrasmuodoltansa (ablative singular)
supistetultansa porrasmuodoltaan (ablative singular)
supistetultansa porrasmuodoltansa (ablative singular)
supistetuiltaan porrasmuodoiltaan (ablative plural)
supistetuiltaan porrasmuodoiltansa (ablative plural)
supistetuiltansa porrasmuodoiltaan (ablative plural)
supistetuiltansa porrasmuodoiltansa (ablative plural)
supistetulleen porrasmuodolleen (allative singular)
supistetulleen porrasmuodollensa (allative singular)
supistetullensa porrasmuodolleen (allative singular)
supistetullensa porrasmuodollensa (allative singular)
supistetuilleen porrasmuodoilleen (allative plural)
supistetuilleen porrasmuodoillensa (allative plural)
supistetuillensa porrasmuodoilleen (allative plural)
supistetuillensa porrasmuodoillensa (allative plural)
supistettunaan porrasmuotonaan (essive singular)
supistettunaan porrasmuotonansa (essive singular)
supistettunansa porrasmuotonaan (essive singular)
supistettunansa porrasmuotonansa (essive singular)
supistettuinaan porrasmuotoinaan (essive plural)
supistettuinaan porrasmuotoinansa (essive plural)
supistettuinansa porrasmuotoinaan (essive plural)
supistettuinansa porrasmuotoinansa (essive plural)
supistetukseen porrasmuodokseen (singular translative)
supistetukseen porrasmuodoksensa (singular translative)
supistetuksensa porrasmuodokseen (singular translative)
supistetuksensa porrasmuodoksensa (singular translative)
supistetuikseen porrasmuodoikseen (plural translative)
supistetuikseen porrasmuodoiksensa (plural translative)
supistetuiksensa porrasmuodoikseen (plural translative)
supistetuiksensa porrasmuodoiksensa (plural translative)
supistetuttaan porrasmuodottaan (abessive singular)
supistetuttaan porrasmuodottansa (abessive singular)
supistetuttansa porrasmuodottaan (abessive singular)
supistetuttansa porrasmuodottansa (abessive singular)
supistetuittaan porrasmuodoittaan (abessive plural)
supistetuittaan porrasmuodoittansa (abessive plural)
supistetuittansa porrasmuodoittaan (abessive plural)
supistetuittansa porrasmuodoittansa (abessive plural)
supistettuineen porrasmuotoineen (comitative plural)
supistettuineen porrasmuotoinensa (comitative plural)
supistettuinensa porrasmuotoineen (comitative plural)
supistettuinensa porrasmuotoinensa (comitative plural)

[ˈs̠upis̠ˌte̞t̪ːup̚ ˈpo̞rːɑ̝s̠ˌmuo̞̯t̪o̞]

reduced row echelon form
reduced row echelon form


variable indépendante

variable indépendante f (plural variables indépendantes)

independent variable
independent variable

(algebra) independent variable (in an equation, any variable whose value is not dependent on any other in the equation)


variable dépendante

variable dépendante f (plural variables dépendantes)

(algebra) dependent variable (in an equation, the variable whose value depends on one or more variables in the equation)


grupa abelowa

grupa abelowa (nominative singular)
grupy abelowe (nominative plural)
grupy abelowej (genitive singular)
grup abelowych (genitive plural)
grupie abelowej (dative singular)
grupom abelowym (dative plural)
grupę abelową (accusative singular)
grupy abelowe (accusative plural)
grupą abelową (instrumental singular)
grupami abelowymi (instrumental plural)
grupie abelowej (locative singular)
grupach abelowych (locative plural)
grupo abelowa (singular vocative)
grupy abelowe (plural vocative)

Literally, “abelian group,” named after Norwegian mathematician Niels Henrik Abel.

named-after

(algebra) abelian group, commutative group


endomorfizm

endomorfizm (nominative singular)
endomorfizmy (nominative plural)
endomorfizmu (genitive singular)
endomorfizmów (genitive plural)
endomorfizmowi (dative singular)
endomorfizmom (dative plural)
endomorfizm (accusative singular)
endomorfizmy (accusative plural)
endomorfizmem (instrumental singular)
endomorfizmami (instrumental plural)
endomorfizmie (locative singular)
endomorfizmach (locative plural)
endomorfizmie (singular vocative)
endomorfizmy (plural vocative)

Compare English endomorphism, French endomorphisme, German Endomorphismus.

(algebra) endomorphism (homomorphism mapping a system to itself)


Abel's theorem

(mathematics, algebra) A theorem that relates a limit of a power series to the sum of its coefficients.


Kerper

/ˈkʰe̞ɐ̯b̥ːɐ/

From Middle High German korper, körper, körpel, from Latin corpor-, inflected stem of corpus.

(algebra) field (algebraic structure with addition and multiplication)


昇冪

ja-noun

昇(しょう)冪(べき) • (shōbeki) ^(←しようべき (syoubeki)?)

昇冪 (canonical)
shōbeki (romanization)
syoubeki (romanization)
しようべき (hiragana historical)


ܡܟܢܫ

aii-verb

ܡܟܲܢܸܫ • (mkanniš)

ܡܟܲܢܸܫ (canonical)
mkanniš (romanization)
ܡܟܲܢܘܿܫܹܐ (gerund)
ܟܘܼܢܵܫܵܐ (noun-from-verb)
ܡܟܘܼܢܫܵܐ (masculine participle passive singular)
ܡܟܘܼܢܫܹ̈ܐ (masculine participle passive plural)
ܡܟܘܼܢܲܫܬܵܐ (feminine participle passive singular)
ܡܟܘܼܢܫܹ̈ܐ (feminine participle passive plural)
ܡܟܲܢܫܵܢܵܐ (masculine singular)
ܡܟܲܢܫܵܢܹ̈ܐ (masculine plural)
ܡܟܲܢܫܵܢܝܼܬ݂ܵܐ (feminine singular)
ܡܟܲܢܫܵܢ̈ܝܵܬ݂ܵܐ (feminine plural)
ܟܲܢܲܫܬܵܐ (singular)
ܟܲܢܲܫ̈ܝܵܬ݂ܵܐ (plural)
ܡܟܘܼܢܸܫ ܠܝܼ (first-person masculine past singular)
ܡܟܘܼܢܸܫ ܠܘܼܟ݂ (masculine past second-person singular)
ܡܟܘܼܢܸܫ ܠܹܗ (masculine past singular third-person)
ܡܟܘܼܢܸܫ ܠܲܢ (first-person masculine past plural)
ܡܟܘܼܢܸܫ ܠܲܘܟ݂ܘܿܢ (masculine past plural second-person)
ܡܟܘܼܢܸܫ ܠܗܘܿܢ (masculine past plural third-person)
ܡܟܘܼܢܸܫ ܠܝܼ (feminine first-person past singular)
ܡܟܘܼܢܸܫ ܠܵܟ݂ܝ (feminine past second-person singular)
ܡܟܘܼܢܸܫ ܠܵܗ̇ (feminine past singular third-person)
ܡܟܘܼܢܸܫ ܠܲܢ (feminine first-person past plural)
ܡܟܘܼܢܸܫ ܠܲܘܟ݂ܘܿܢ (feminine past plural second-person)
ܡܟܘܼܢܸܫ ܠܗܘܿܢ (feminine past plural third-person)
ܡܟܲܢܫܸܢ (first-person masculine singular)
ܡܟܲܢܫܸܬ (masculine second-person singular)
ܡܟܲܢܸܫ (masculine singular third-person)
ܡܟܲܢܫܲܚ (first-person masculine plural)
ܡܟܲܢܫܝܼܬܘܿܢ (masculine plural second-person)
ܡܟܲܢܫܝܼ (masculine plural third-person)
ܡܟܲܢܫܲܢ (feminine first-person singular)
ܡܟܲܢܫܵܬܝ (feminine second-person singular)
ܡܟܲܢܫܵܐ (feminine singular third-person)
ܡܟܲܢܫܲܚ (feminine first-person plural)
ܡܟܲܢܫܝܼܬܘܿܢ (feminine plural second-person)
ܡܟܲܢܫܝܼ (feminine plural third-person)
ܡܟܘܼܢܫܸܢ (first-person masculine singular)
ܡܟܘܼܢܫܸܬ (masculine second-person singular)
ܡܟܘܼܢܸܫ (masculine singular third-person)
ܡܟܘܼܢܫܸܚ (first-person masculine plural)
ܡܟܘܼܢܫܝܼܬܘܿܢ (masculine plural second-person)
ܡܟܘܼܢܫܝܼ (masculine plural third-person)
ܡܟܘܼܢܫܲܢ (feminine first-person singular)
ܡܟܘܼܢܫܲܬܝ (feminine second-person singular)
ܡܟܘܼܢܫܵܐ (feminine singular third-person)
ܡܟܘܼܢܫܸܚ (feminine first-person plural)
ܡܟܘܼܢܫܝܼܬܘܿܢ (feminine plural second-person)
ܡܟܘܼܢܫܝܼ (feminine plural third-person)
ܟܲܢܸܫ (imperative masculine second-person singular)
ܟܲܢܫܘܼܢ (imperative masculine plural second-person)
ܟܲܢܸܫܝ (feminine imperative second-person singular)
ܟܲܢܫܘܼܢ (feminine imperative plural second-person)

Intensitive stem of the verb ܟܵܢܹܫ (kānēš).


finitely generated

From the study of generators. The motivation for calling topologies satisfying sense 1.5 "finitely generated" is that any topology satisfies sense 1.5 if and only if it is coherent with its finite subspaces. Thus, metaphorically, it is "generated" by them. The category-theoretic senses were created to generalize those of abstract algebra, and so were named identically.

(algebra) In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

(most generally, category theory, of an object X in a locally small category 𝒞 that admits filtered colimits of monomorphism) Such that the functor operatorname Hom_( mathcal )C(X,·) preserves those filtered colimits of monomorphisms.

(less generally, but still covering most cases outside pure category theory, of an object X in a concrete category) Being a quotient object of a free object over a finite set, i.e. being the target of a regular epimorphism from an object which is free on a finite set.

less generally; but still covering most cases outside pure category theory; less generally; but still covering most cases outside pure category theory

(abstract algebra, of a group-like structure: a group, module, ring, monoid, etc.) Having a finite set of generators, i.e. having a finite set of elements from which all other elements can be created in finitely many steps under the permitted operations (viz. the group operation for groups, addition and scalar multiplication for modules, addition and multiplication for rings, etc.)

(ring theory, of a (left) ideal in a ring R) Finitely generated as a (left) module over R.

(of a space) Equipped with an Alexandrov topology (i.e. one where the intersection of every family of open sets is open).


formal sum

(mathematics) An expression which looks like a sum but where the symbol + has a purely symbolic role, in the sense that the summands cannot be meaningfully combined.

(algebra) An element of a free abelian group or vector space regarded as a sum of basis elements.


associated prime

en-noun

associated prime (plural associated primes)

(algebra, of a module M over a ring R) A ideal of R which is the annihilator of some prime submodule of M.

(commutative algebra) If the ring R is commutative, equivalently: A prime ideal of R which is the annihilator of some element of M.


prime subring

The image of the homomorphism ℤ→ R is called the prime subring of R. Clearly ch(R) = 0 ⟷ the prime subring of R is isomorphic to ℤ.

2006, Shreeram Shankar Abhyankar, The Algebraic Structure of Crossed Products, World Scientific, page 21:

The image of the morphism f_A is the prime subring of A. The prime subring is either isomorphic to the ring ℤ or isomorphic to the ring ℤ/nℤ for some n > 0.

2013, Michel Broué, Some Topics in Algebra: An Advanced Undergraduate Course at PKU, Springer Science & Business Media, page 10:

(algebra, ring theory, of a (unital) ring R) The image of the natural homomorphism from ℤ into R, which is the unique homomorphism mapping 1_ℤ to 1_R. Equivalently, the intersection of all subrings of R.


Bézout domain

So-called because such domains satisfy Bézout's identity, in turn named after Étienne Bézout.

(algebra, ring theory) An integral domain in which the sum of two principal ideals is also a principal ideal.


lie above

en-verb

lie above (third-person singular simple present lies above, present participle lying above, simple past lay above, past participle lain above)

lies above (present singular third-person)
lying above (participle present)
lay above (past)
lain above (participle past)

If p₁, p ∈ Spec(A) with p₁ ⊂ p, and if q₁ ∈ Spec(B) lies above p₁, then there exists q ∈ Spec(B) which lies above p and such that q₁ ⊂ q.

2007, Meinolf Geck, Group Representation Theory, EPFL Press, page 199:

(algebra, ring theory) Synonym of lie over.


discrete valuation ring

en-noun

discrete valuation ring (plural discrete valuation rings)

(algebra, ring theory) A local principal ideal domain whose unique maximal ideal is not the zero ideal.


zero ideal

(algebra, ring theory, of a ring) The ideal containing only the element zero.


comaximal

LL-Q1860 (eng)-Flame, not lame-comaximal.wav

Two proper ideals I and J of R are said to be comaximal (or I is comaximal to J) if I + J = R.

2001, László Fuchs, Luigi Salce, Modules over Non-Noetherian Domains, American Mathematical Society, page 3:

(algebra, ring theory, of two ideals) Synonym of coprime.


digri

digrí (canonical)
ᜇᜒᜄ᜔ᜇᜒ (Baybayin)
degri (alternative)

Borrowed from English degree, from Middle English degre, from Old French degré, from Old French de- + Latin gradus.

(algebra) degree (the maximal exponent of a polynomial)


三次方程式

ㄙㄢ ㄘˋ ㄈㄤ ㄔㄥˊ ㄕˋ

ㄙㄢ ㄘˋ ㄈㄤ ㄔㄥˊ ㄕˋ

саньцы фанчэнши

/sän⁵⁵ t͡sʰz̩⁵¹ fɑŋ⁵⁵ ʈ͡ʂʰɤŋ³⁵ ʂʐ̩⁵¹/

/sän⁵⁵ t͡sʰz̩⁵¹ fɑŋ⁵⁵ ʈ͡ʂʰɤŋ³⁵ ʂʐ̩⁵¹/


三次方程式

ja-noun

三(さん)次(じ)方(ほう)程(てい)式(しき) • (sanji hōteishiki) ^(←さんじはうていしき (sanzi fauteisiki)?)

三次方程式 (canonical)
sanji hōteishiki (romanization)
sanzi fauteisiki (romanization)
さんじはうていしき (hiragana historical)

[sã̠ɲ̟d͡ʑi ho̞ːte̞ːɕi̥kʲi]

三(さん)次(じ) (sanji, “third-degree; cubic”) + 方(ほう)程(てい)式(しき) (hōteishiki, “equation”).