Hi. I'm trying to prove this "little fact": let M, N be finitely generated modules over a PID. Then if M+M=N+N (where = means isomorphism and + means direct sum) then M=N.(adsbygoogle = window.adsbygoogle || []).push({});

I'm sure it can be done with the structure theorem (it is obvious from the hypotheses); it looks like it should be trivially proven, but alas, I don't think it can be.

What do you think?

Cheers,

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# Modules: M+M = N+N then M=N

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