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Tensor product-definition-balanced versus bilinear maps

When defining tensor products $M\otimes_R N$ over a commutative ring $R$ one can use a universal property with respect to bilinear maps $M\times N\rightarrow P$, for any $R$-module $P$. On the other …
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Tensor product-definition-balanced versus bilinear maps

I guess I have a counterexample. Let $G$ be an abelian group and form the group algebra $kG$ which is commutative. Pick any $kG$-module $M$ and define a structure of module on the dual $M^*$ via $[g …
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