Definition:Ring Action Defined by Ring Representation

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Definition

Let $R$ be a ring.

Let $M$ be an abelian group.

Let $\rho : R \to \map {\operatorname {End} } M$ be a ring representation.


The associated (left) ring action is the linear ring action:

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


Also see