"division algebra" meaning in All languages combined

See division algebra on Wiktionary

Noun [English]

Forms: division algebras [plural]
Head templates: {{en-noun}} division algebra (plural division algebras)
  1. (algebra) A linear algebra such that its non-zero vectors form a multiplicative group. Synonyms: associative division algebra Hypernyms: associative algebra, linear algebra, division ring, vector space Hyponyms: field, quaternions, complex numbers, reals
    Sense id: en-division_algebra-en-noun-vLA0cM~S Categories (other): Algebra Topics: algebra, mathematics, sciences
  2. (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.) Hypernyms: algebra over a field, ring, vector space Hyponyms: octonions
    Sense id: en-division_algebra-en-noun-9hoAG4M9 Categories (other): Algebra, English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 25 75 Disambiguation of Pages with 1 entry: 24 76 Disambiguation of Pages with entries: 23 77 Topics: algebra, mathematics, sciences

Inflected forms

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        "(algebra) A linear algebra such that its non-zero vectors form a multiplicative group."
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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 2026-09-25 from the enwiktionary dump dated 2026-09-02 using wiktextract (1a05e46 and e3d6d4e). 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.