algebra over a ring English

Meaning algebra over a ring meaning

What does algebra over a ring mean?

algebra over a ring noun

— (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.)