associative algebra

English

Noun

associative algebra (plural associative algebras)

1. (algebra) A vector space over some field which also has an associative vector-valued multiplication operator between vectors which together with the abelian group feature of the vector space makes a ring.

   Synonym: linear algebra

   Antonym: non-associative algebra

   Hypernyms: algebra over a field, non-associative algebra

   Hyponyms: algebraic number field, Boolean ring, tensor algebra, matrix algebra, Lie algebra, polynomial ring, polynomial algebra, Grassmann algebra, Clifford algebra, geometric algebra, central simple algebra, algebraic extension

2. (algebra) A module over a ring together with an associative bilinear module-element-valued operator between module elements which together with the abelian group feature of the module makes a ring.

   Synonym: linear algebra

   Antonym: non-associative algebra

   Hypernyms: algebra over a ring, non-associative algebra

   Hyponyms: algebraic number field, Boolean ring, tensor algebra, matrix algebra, polynomial ring, polynomial algebra, Grassmann algebra, geometric algebra