Definition:Unitary Module

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

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

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

Also known as
A unitary module is also known as a unital module. A unitary module over $R$ can also be referred to as a  unitary $R$-module.

Also see

 * Definition:Module