Associated primes of a sum of modules - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-18T07:19:47Z http://mathoverflow.net/feeds/question/78297 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/78297/associated-primes-of-a-sum-of-modules Associated primes of a sum of modules Mars II 2011-10-16T23:45:40Z 2011-10-16T23:45:40Z <p>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.</p> <p>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.</p>