algebra over a ring

English

Noun

algebra over a ring (plural algebras over rings)

1. (algebra) A module (over some ring) with an additional binary operation, a module-element-valued product between module elements, which is bilinear over module addition and scalar multiplication. (N.B.: such bilinearity implies distributivity of the module multiplication with respect to the module addition, which means that such a module is also a ring.)

Synonyms

• R-algebra

Hyponyms

• associative algebra
• non-associative algebra
• group ring

Related terms

• algebra over a field