Asymptotic stability of
Abstract: 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 defined by . We shall prove:
(1) For n sufficiently large, is independent of n.
We moreover give two examples concerning the behavior of .
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Keywords: Associated prime ideals, associated graded rings and modules
Article copyright: © Copyright 1979 American Mathematical Society