\begin{definition}[Definition:Ring Representation/Unital]
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 $R \to \map {\operatorname {End} } M$ which is unital.
That is, it is a unital ring homomorphism from $R$ to the endomorphism ring $\map {\operatorname {End} } M$.
\end{definition}