Definition:Ring Representation Defined by Ring Action
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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:
- $\map {\map \rho r} m = \map \phi {r, m}$