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.)
A branch of mathematics dealing with equational classes of algebras, where similar theorems from disparate branches of algebra are unified.
An algebraic structure studied therein.