division algebra

== English == === Noun === division algebra (plural division algebras) (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 (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