Can anyone tell me where I can read a proof that the natural map
$Hom_{A}(M,N)[S^{-1}]\rightarrow Hom_{A[S^{-1}]}(M[S^{-1}],N[S^{-1}])$
is an isomorphism if $M$ is finitely presented?
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$\begingroup$ This is a) an easy exercise, b) standard material, for example included in Bourbaki's book on commutative algebra. In any case it is not appropriate for mathoverflow. $\endgroup$– Martin BrandenburgCommented Mar 13, 2012 at 14:31
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Yes. You can read a proof of this fact at:
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1$\begingroup$ @Ramsey: When easy question are answered, other questions of this type will occur again. $\endgroup$ Commented Mar 13, 2012 at 14:32
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1$\begingroup$ I was kind of hoping that the terse reference to MSE would be taken as a bit of a hint that this question would be better asked there. $\endgroup$– RamseyCommented Mar 13, 2012 at 14:43
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2$\begingroup$ Ramsey: I see what you were thinking (and can imagine thinking the same way myself), but I suspect this sort of subtlety is likely to be lost on anybody who is too intellectually lazy to do his own homework. $\endgroup$ Commented Mar 13, 2012 at 16:07
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1$\begingroup$ Steven, that's pretty harsh. This could be a research mathematician who is asking a question outside his/her field, and not necessarily an "intellectually lazy" student. The OP might not have realized that it's regarded as an easy question. $\endgroup$ Commented Mar 13, 2012 at 17:01