See division algebra on Wiktionary
{ "forms": [ { "form": "division algebras", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "division algebra (plural division algebras)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "A linear algebra such that its non-zero vectors form a multiplicative group." ], "hyponyms": [ { "word": "field" }, { "word": "quaternions" }, { "word": "complex numbers" }, { "word": "reals" } ], "id": "en-division_algebra-en-noun-vLA0cM~S", "links": [ [ "algebra", "algebra" ], [ "multiplicative", "multiplicative" ], [ "group", "group" ] ], "raw_glosses": [ "(algebra) A linear algebra such that its non-zero vectors form a multiplicative group." ], "synonyms": [ { "word": "associative division algebra" } ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "25 75", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "23 77", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" } ], "glosses": [ "An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element.)" ], "hyponyms": [ { "word": "octonions" } ], "id": "en-division_algebra-en-noun-9hoAG4M9", "links": [ [ "algebra", "algebra" ] ], "raw_glosses": [ "(algebra) An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element.)" ], "topics": [ "algebra", "mathematics", "sciences" ] } ], "wikipedia": [ "division algebra" ], "word": "division algebra" }
{ "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "Pages with 1 entry", "Pages with entries" ], "forms": [ { "form": "division algebras", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "division algebra (plural division algebras)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "en:Algebra" ], "glosses": [ "A linear algebra such that its non-zero vectors form a multiplicative group." ], "hyponyms": [ { "word": "field" }, { "word": "quaternions" }, { "word": "complex numbers" }, { "word": "reals" } ], "links": [ [ "algebra", "algebra" ], [ "multiplicative", "multiplicative" ], [ "group", "group" ] ], "raw_glosses": [ "(algebra) A linear algebra such that its non-zero vectors form a multiplicative group." ], "synonyms": [ { "word": "associative division algebra" } ], "topics": [ "algebra", "mathematics", "sciences" ] }, { "categories": [ "en:Algebra" ], "glosses": [ "An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element.)" ], "hyponyms": [ { "word": "octonions" } ], "links": [ [ "algebra", "algebra" ] ], "raw_glosses": [ "(algebra) An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element.)" ], "topics": [ "algebra", "mathematics", "sciences" ] } ], "wikipedia": [ "division algebra" ], "word": "division algebra" }
Download raw JSONL data for division algebra meaning in All languages combined (1.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.