Axiom:Left Module Axioms

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 with one operation $\left({G, +_G, \circ}\right)_R$ which satisfies the following conditions:

These stipulations are called the left module axioms.

Also known as
Some sources do not distinguish between a left module and a right module, and instead refer to these axioms as the module axioms.

Also see

 * Definition:Right Module Axioms
 * Definition:Module