"commutative algebra" meaning in All languages combined

See commutative algebra on Wiktionary

Noun [English]

Forms: commutative algebras [plural]
Head templates: {{en-noun|~}} commutative algebra (countable and uncountable, plural commutative algebras)
  1. (mathematics) The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules). Tags: countable, uncountable Categories (topical): Mathematics Translations (branch of mathematics): algebra commutativa [feminine] (Italian), álgebra comutativa [feminine] (Portuguese), коммутати́вная а́лгебра (kommutatívnaja álgebra) [feminine] (Russian)
    Sense id: en-commutative_algebra-en-noun-Vi8~UXZ- Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 47 53 Disambiguation of Pages with 1 entry: 49 51 Disambiguation of Pages with entries: 48 52 Topics: mathematics, sciences Disambiguation of 'branch of mathematics': 70 30
  2. (algebra) Any algebra (mathematical structure) in which the multiplication operation is commutative. Tags: countable, uncountable Categories (topical): Algebra Synonyms (algebra which has a commutative multiplication operation): Abelian algebra Hyponyms: polynomial ring Translations (algebra in which multiplication is commutative): algebra commutativa [feminine] (Italian), álgebra comutativa [feminine] (Portuguese), коммутати́вная а́лгебра (kommutatívnaja álgebra) [feminine] (Russian)
    Sense id: en-commutative_algebra-en-noun-LlROC-97 Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Italian translations, Terms with Portuguese translations, Terms with Russian translations Disambiguation of English entries with incorrect language header: 47 53 Disambiguation of Entries with translation boxes: 29 71 Disambiguation of Pages with 1 entry: 49 51 Disambiguation of Pages with entries: 48 52 Disambiguation of Terms with Italian translations: 40 60 Disambiguation of Terms with Portuguese translations: 41 59 Disambiguation of Terms with Russian translations: 41 59 Topics: algebra, mathematics, sciences Disambiguation of 'algebra which has a commutative multiplication operation': 28 72 Disambiguation of 'algebra in which multiplication is commutative': 29 71
The following are not (yet) sense-disambiguated
Related terms: noncommutative algebra (english: concerned with rings that are not assumed to be commutative)

Inflected forms

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          "text": "2003, Ragnar-Olaf Buchweitz, Morita contexts, idempotents, and Hochschild cohomology — with applications to invariant rings, Luchezar L. Avramov, Marcel Morales, Marc Chardin, Claudia Polini (editors), Commutative Algebra: Interactions with Algebraic Geometry: International Conference, American Mathematical Society, page 27,\nIt is not until section 7 that we deal with commutative algebra proper, whereas the sections leading up to it should be seen as advocacy that excursions into noncommutative algebra can help to shed light on problems in commutative algebra."
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          "text": "Theorem. If the complex of the linearly independent numbers of the form #x5C;zetaa-a#x5C;zeta be deleted from an algebra, the remaining numbers form a commutative algebra.",
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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