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We study, in certain cases, the notions of finiteness and stability of the set of associated primes and vanishing of the homogeneous pieces of graded generalized local cohomology modules.
Let R be a commutative multiplication ring and let N be a non-zero finitely generated multiplication R-module. We characterize certain prime submodules of N. Also, we show that N is Cohen-Macaulay whenever R is Noetherian.
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