division algebra

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Noun

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division algebra (plural division algebras)

  1. (algebra) A linear algebra such that its non-zero vectors form a multiplicative group.
    Synonym: associative division algebra
    Hypernyms: associative algebra, linear algebra, division ring, vector space
    Hyponyms: field, quaternions, complex numbers, reals
  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
    Hyponym: octonions