Definition:Ring Representation Defined by Ring Action

Definition
Let $R$ be a ring.

Let $M$ be an abelian group.

Let $\phi : R \times M \to M$ be a left linear ring action.

The associated ring representation is the ring representation $\rho : R \to \operatorname{End}(M)$ with:
 * $\rho(r)(m) = \phi(r, m)$

Also see

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