Throughout this post, I consider "R-module" and "representation of R" to be the same.(adsbygoogle = window.adsbygoogle || []).push({});

Similarly, I consider "A-module" and "representation of A" to be the same.

I define of a representation of a unital ring R as an Abelian group M together with a homomorphism from R to the unital ring of endomorphisms of M.

I define of a representation of a unital associative algebra A as a vector space V together with a homomorphism from A to the unital associative algebra of endomorphisms of V.

Question:

Is it so that the notion of a representation of a unital associative algebra generalises the notion of a representation of a unital ring? I think I've heard this result, but can't find it by a Google search.

It would seem strange if it were true, since the notion of a unital ring actually generalizes the notion of a unital associative algebra.

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# Algebra-Modules generalize Ring-Modules?

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