See additive group on Wiktionary
{ "forms": [ { "form": "additive groups", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "additive group (plural additive groups)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Group theory", "orig": "en:Group theory", "parents": [ "Algebra", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "Any (often, but not necessarily, abelian) group whose binary operation is called addition." ], "id": "en-additive_group-en-noun-XZp8IiJL", "links": [ [ "mathematics", "mathematics" ], [ "group", "group" ], [ "binary operation", "binary operation" ], [ "addition", "addition" ], [ "+", "+" ], [ "group theory", "group theory" ], [ "abelian", "abelian" ] ], "raw_glosses": [ "(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "(group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition." ], "topics": [ "group-theory", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition." ], "id": "en-additive_group-en-noun-idz4JVPx", "links": [ [ "mathematics", "mathematics" ], [ "group", "group" ], [ "binary operation", "binary operation" ], [ "addition", "addition" ], [ "+", "+" ], [ "algebra", "algebra" ], [ "ring", "ring" ], [ "field", "field" ], [ "vector space", "vector space" ], [ "commutative", "commutative" ], [ "operation", "operation" ] ], "raw_glosses": [ "(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "(algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition." ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Category theory", "orig": "en:Category theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "27 23 50", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "30 29 41", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "27 25 48", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "27 24 50", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "31 27 42", "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w+disamb" }, { "_dis": "30 26 45", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "30 26 45", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "28 25 47", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition." ], "id": "en-additive_group-en-noun-9-Y5KRSr", "links": [ [ "mathematics", "mathematics" ], [ "group", "group" ], [ "binary operation", "binary operation" ], [ "addition", "addition" ], [ "+", "+" ], [ "category theory", "category theory" ], [ "group object", "group object" ], [ "group functor", "group functor" ], [ "group scheme", "group scheme" ] ], "raw_glosses": [ "(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "(category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition." ], "topics": [ "category-theory", "computing", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ] } ], "translations": [ { "_dis1": "33 33 34", "code": "fi", "lang": "Finnish", "sense": "group or algebraic object regarded as a group with operation called addition", "word": "additiivinen ryhmä" }, { "_dis1": "33 33 34", "code": "fi", "lang": "Finnish", "sense": "group or algebraic object regarded as a group with operation called addition", "word": "yhteenlaskuryhmä" }, { "_dis1": "33 33 34", "code": "fr", "lang": "French", "sense": "group or algebraic object regarded as a group with operation called addition", "tags": [ "masculine" ], "word": "groupe additif" }, { "_dis1": "33 33 34", "code": "de", "lang": "German", "sense": "group or algebraic object regarded as a group with operation called addition", "tags": [ "feminine" ], "word": "additive Gruppe" }, { "_dis1": "33 33 34", "code": "es", "lang": "Spanish", "sense": "group or algebraic object regarded as a group with operation called addition", "tags": [ "masculine" ], "word": "grupo aditivo" } ], "wikipedia": [ "additive group" ], "word": "additive group" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Spanish translations" ], "forms": [ { "form": "additive groups", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "additive group (plural additive groups)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "en:Group theory", "en:Mathematics" ], "glosses": [ "Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "Any (often, but not necessarily, abelian) group whose binary operation is called addition." ], "links": [ [ "mathematics", "mathematics" ], [ "group", "group" ], [ "binary operation", "binary operation" ], [ "addition", "addition" ], [ "+", "+" ], [ "group theory", "group theory" ], [ "abelian", "abelian" ] ], "raw_glosses": [ "(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "(group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition." ], "topics": [ "group-theory", "mathematics", "sciences" ] }, { "categories": [ "en:Algebra", "en:Mathematics" ], "glosses": [ "Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition." ], "links": [ [ "mathematics", "mathematics" ], [ "group", "group" ], [ "binary operation", "binary operation" ], [ "addition", "addition" ], [ "+", "+" ], [ "algebra", "algebra" ], [ "ring", "ring" ], [ "field", "field" ], [ "vector space", "vector space" ], [ "commutative", "commutative" ], [ "operation", "operation" ] ], "raw_glosses": [ "(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "(algebra) Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition." ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ "en:Category theory", "en:Mathematics" ], "glosses": [ "Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition." ], "links": [ [ "mathematics", "mathematics" ], [ "group", "group" ], [ "binary operation", "binary operation" ], [ "addition", "addition" ], [ "+", "+" ], [ "category theory", "category theory" ], [ "group object", "group object" ], [ "group functor", "group functor" ], [ "group scheme", "group scheme" ] ], "raw_glosses": [ "(mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:", "(category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition." ], "topics": [ "category-theory", "computing", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ] } ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "group or algebraic object regarded as a group with operation called addition", "word": "additiivinen ryhmä" }, { "code": "fi", "lang": "Finnish", "sense": "group or algebraic object regarded as a group with operation called addition", "word": "yhteenlaskuryhmä" }, { "code": "fr", "lang": "French", "sense": "group or algebraic object regarded as a group with operation called addition", "tags": [ "masculine" ], "word": "groupe additif" }, { "code": "de", "lang": "German", "sense": "group or algebraic object regarded as a group with operation called addition", "tags": [ "feminine" ], "word": "additive Gruppe" }, { "code": "es", "lang": "Spanish", "sense": "group or algebraic object regarded as a group with operation called addition", "tags": [ "masculine" ], "word": "grupo aditivo" } ], "wikipedia": [ "additive group" ], "word": "additive group" }
Download raw JSONL data for additive group meaning in All languages combined (4.3kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-15 from the enwiktionary dump dated 2024-12-04 using wiktextract (8a39820 and 4401a4c). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.