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 $\rho: R \to \map {\operatorname {End} } M$ with:

$\map {\map \rho r} m = \map \phi {r, m}$

Also see

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