Axiom:Unitary Module Axioms

Definition
Let $\struct {R, +_R, \times_R}$ be a ring with unity whose unity is $1_R$.

Let $\struct {G, +_G}$ be an abelian group.

A unitary module over $R$ is an $R$-algebraic structure with one operation $\struct {G, +_G, \circ}_R$ which satisfies the following conditions:

These stipulations are called the unitary module axioms.

Also see

 * Definition:Module
 * Definition:Unitary Module