Definition:Ring Representation

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Definition

Let $R$ be a ring.

Let $M$ be an abelian group.


A ring representation of $R$ on $M$ is a ring homomorphism from $R$ to the endomorphism ring $\map {\operatorname {End} } M$.


Unital Ring Representation

Let $R$ be a ring with unity.

Let $M$ be an abelian group.


A unital ring representation of $R$ on $M$ is a ring representation $R \to \map {\operatorname {End} } M$ which is unital.

That is, it is a unital ring homomorphism from $R$ to the endomorphism ring $\map {\operatorname {End} } M$.


Also see


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