division algebra

English

Noun

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