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Oct 24, 2012 at 7:44 comment added Laurent Berger @Charles : yes, sorry, I forgot to say "free", so the modules should be free of the same rank. Thanks.
Oct 23, 2012 at 19:29 comment added Charles Staats I think you need additional hypotheses: the modules need to be finitely generated, and probably isomorphic (or free, which implies isomorphic given they have the same rank). An interesting note is that the ring need not be noetherian.
Oct 23, 2012 at 18:37 comment added Todd Trimble +1. I find this fact particularly useful.
Oct 23, 2012 at 17:33 history answered Laurent Berger CC BY-SA 3.0