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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Asymptotic stability of $ {\rm Ass}(M/I\sp{n}M)$


Author: M. Brodmann
Journal: Proc. Amer. Math. Soc. 74 (1979), 16-18
MSC: Primary 13E05
MathSciNet review: 521865
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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 $ {\text{Spec}}(R)$ defined by $ A(n) = {\text{Ass}_R}(M/{I^n}M)$. We shall prove:

(1) For n sufficiently large, $ A(n)$ is independent of n.

We moreover give two examples concerning the behavior of $ A(n)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0521865-8
PII: S 0002-9939(1979)0521865-8
Keywords: Associated prime ideals, associated graded rings and modules
Article copyright: © Copyright 1979 American Mathematical Society