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I have to demonstrate that $R$ viewed as left $R$-module is a progenerator (i.e. a projective and finitely generated generator) of $R$-mod, the category of left $R$-modules.

How can I do this? I know that a left $R$-module $M$ is a generator of $R$-mod if and only if $M^n$ is the direct sum of $R$ and $R'$ for some integer $n>1$ and some $R$-module $R'$. Thanks!

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