Definition:Right Ring Action Defined by Ring Antirepresentation

Definition
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:
 * $M \times R \to M$:
 * $\tuple {m, r} \mapsto \map \rho r \paren m$

Also see

 * Definition:Ring Action Defined by Ring Representation
 * Definition:Ring Antirepresentation Defined by Right Ring Action
 * Correspondence between Linear Ring Actions and Ring Representations