Abstract
Let R be a (not necessarily Noetherian) commutative ring and let M be a (not necessarily finitely generated) R-module. We characterize the modules with only finitely many weakly associated primes as those modules M admitting a chain 0 = M0 ⊂ M1 ⊂ ... ⊂ Mn = M of submodules together with prime ideals p1, p2,...,pn such that the set of weakly associated primes of Mi/Mi-1 is equal to {pi} for all 1 ≦ i ≦ n. Let M = gra(M) = ⊕n≧0anM/an+1M be the corresponding graded module over the graded ring R = gra(R) = ⊕n≧0an/an+1. It is shown that the union of the set of weakly associated primes of.....
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