Definition:Ring Representation

Definition
Let $R$ be a commutative ring.

Let $M$ be an abelian group.

A ring representation of $R$ on $M$ is a ring homomorphism from $R$ to the endomorphism ring of $M$.

Unital Ring Representation
Let $R$ be a commutative ring with unity.

A unital ring representation of $R$ on $M$ is a unital ring homomorphism from $R$ to the endomorphism ring of $M$.

Also see

 * Definition:Module over Ring