Definition:Left Module

Definition
Let $\left({R, +_R, \times_R}\right)$ be a ring.

Let $\left({G, +_G}\right)$ be an abelian group.

A left module over $R$ is an $R$-algebraic structure $\left({G, +_G, \circ}\right)_R$ with one operation $\circ$, the (left) ring action, which satisfies the left module axioms:

Also see

 * Definition:Right Module
 * Definition:Module