## On tensor product [closed]

Let $\alpha\colon G\to H$ be a group homomorphism and $R$ be a commutative ring. Regard $R$ as $RN$-module with trivial $N$-action.

Further, we denote $N=\operatorname{Ker}\alpha$.

Is it true that $\mathbb{Z}G\otimes_{\mathbb{Z}}R\otimes_{RN}R=RH$ even $\alpha$ is not onto?

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From the looks of it, this seems like a homework question to me! – Somnath Basu Jan 24 2011 at 17:50
I agree, Somnath. – Todd Trimble Jan 24 2011 at 17:59
How is the left hand side supposed to see any difference when $H$ is increased? This seems like too trivial for a homework question to me! – Alex Bartel Jan 24 2011 at 18:03
Dear Alex, I really agree with you. Thank you. – tensorproductgogogle Jan 24 2011 at 18:11