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Post Reopened by Steven Landsburg, Andrey Rekalo, Karl Schwede, Ramiro de la Vega, Yemon Choi
Post Closed as "too localized" by Fernando Muro, Martin Brandenburg, Eric Wofsey, Andreas Blass, Will Sawin
corrected speling
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user30230
user30230

Let $M$ and $N$ be $R$ modules ($R$ commutative with identity). Is it true that if fotfor every prime ideal $P$, $M_P \cong N_P$ (as $R_P$ modules) then $M \cong N$ ? Clearly the question is true if $M$ or $N$ is zero. But what about the non-zero case !?

Let $M$ and $N$ be $R$ modules ($R$ commutative with identity). Is it true that if fot every prime ideal $P$, $M_P \cong N_P$ (as $R_P$ modules) then $M \cong N$ ? Clearly the question is true if $M$ or $N$ is zero. But what about the non-zero case !?

Let $M$ and $N$ be $R$ modules ($R$ commutative with identity). Is it true that if for every prime ideal $P$, $M_P \cong N_P$ (as $R_P$ modules) then $M \cong N$ ? Clearly the question is true if $M$ or $N$ is zero. But what about the non-zero case !?

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user30230
user30230

locally isomorphic modules

Let $M$ and $N$ be $R$ modules ($R$ commutative with identity). Is it true that if fot every prime ideal $P$, $M_P \cong N_P$ (as $R_P$ modules) then $M \cong N$ ? Clearly the question is true if $M$ or $N$ is zero. But what about the non-zero case !?