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Asymptotic Stability of Ass(M/I n M)

Asymptotic Stability of Ass(M/I n M)

Let R be a noetherian ring, I an ideal of R and M a finitely generated R-module.Let A be the map from N into the subsets of Spec(R) defined by A(n) = AssR (M/IIM).We shall prove:(1) For n sufficiently large, A(n) is independent of n.We moreover give two examples concerning …