Definition:Right Ring Action Defined by Ring Antirepresentation
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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 antirepresentation.
The associated right ring action is the right linear ring action:
- $M \times R \to M$:
- $\tuple {m, r} \mapsto \map \rho r \paren m$