algebra over a ring
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English[edit]
Noun[edit]
algebra over a ring (plural algebras over rings)
- (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.)