# how to prove that localisation preserves Hom's [closed]

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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## closed as too localized by Martin Brandenburg, Steven Landsburg, unknown (google), Karl Schwede, Andy PutmanMar 15 '12 at 5:19

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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. –  Martin Brandenburg Mar 13 '12 at 14:31