\begin{definition}[Definition:Right Ring Action Defined by Ring Antirepresentation]
Let $R$ be a ring.
Let $M$ be an abelian group.
Let $\rho: R \to \map {\operatorname {End} } M$ be a ring antirepresentation.
The '''associated right ring action''' is the right linear ring action:
:$M \times R \to M$:
:$\tuple {m, r} \mapsto \map \rho r \paren m$
\end{definition}