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.