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Let $f: S^{-1} M \to S^{-1}A \otimes_A M$ defined by $$m/s \to 1/s \otimes m$$ $g: S^{-1}A \otimes_A M \to S^{-1} M$ defined by $$a/s \otimes m \to am/s $$

Prove that $f$ and $g$ are well defined ?

How can we prove $f$ is an $S^{-1}A$ module homomorphism?

Here $A$ is commutative ring with identity and $M$ is module and $S$ multiplicative subset of $A$.

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    You mean $S$ is a multiplicative *subset* of $A$ ?2012-11-18
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    yes sorry thats what i meant2012-11-18
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    the only problem I have is how to prove that f is well defined ? all the rest is ok2012-11-18

3 Answers 3