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