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edited Apr 13, 2017 at 12:19

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

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created Mar 13, 2012 at 14:23

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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