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Ultrafilter! Waffle! - FLMPotD
March 26th, 2011
02:17 pm

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FLMPotD
Find a commutative ring R, a multiplicative subset S \subset R, and finitely generated R-modules M and N such that the natural map S^{-1}Hom(M,N) \to Hom(S^{-1}M,S^{-1}N) is not an isomorphism.

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From:yuvalwig
Date:March 26th, 2011 07:47 pm (UTC)
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No offense, but these have started sounding suspiciously like Theorems of the Day.
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From:darkerline
Date:March 27th, 2011 06:09 am (UTC)
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Funny, I was about to comment on how this FLMPotD is the first one in a while I feel well-equipped to solve. I didn't actually solve it in the first few minutes I looked at it (I tried coming up with some "simplest possible" example and then my modules ended up not being finitely generated), but maybe I will if I get a bit of spare time in the next couple of days.
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