Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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?

share|improve this question
    
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
add comment

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

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

1 Answer

up vote 1 down vote accepted

Yes. You can read a proof of this fact at:

http://math.stackexchange.com/questions/75812/does-localisation-commute-with-hom-for-finitely-generated-modules

share|improve this answer
1  
@Ramsey: When easy question are answered, other questions of this type will occur again. –  Martin Brandenburg Mar 13 '12 at 14:32
1  
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. –  Ramsey Mar 13 '12 at 14:43
2  
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. –  Steven Landsburg Mar 13 '12 at 16:07
1  
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. –  Todd Trimble Mar 13 '12 at 17:01
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.