Definition:Ring Representation/Unital

Definition
Let $R$ be a ring with unity.

Let $M$ be an abelian group.

A unital ring representation of $R$ on $M$ is a ring representation $R \to \operatorname{End} \left({M}\right)$ which is unital.

That is, it is a unital ring homomorphism from $R$ to the endomorphism ring $\operatorname{End} \left({M}\right)$.

Also see

 * Definition:Unitary Module