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Let M be a module, with M_1 and M_2 submodules such that their sum is M. Is it true in full generality that Ass(M) = Ass(M_1) \cup Ass(M_2). If so prove, if not, provide a counter example.

I believe the statement is false. The fact that Ass(M_i) \subset M is obvious, and i know it holds for a direct sum, however i was hoping someone could clarify with a counter example. Thanks is advance.

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Please do your own homework. – Steven Landsburg Oct 17 2011 at 0:30
Try posting this question in math.stackexchange.com where it may get answers. – Reimundo Heluani Oct 17 2011 at 1:31
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closed as off topic by Andres Caicedo, S. Carnahan♦ Oct 17 2011 at 2:01

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