Asymptotic stability of $\textrm {Ass}(M/I^{n}M)$
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- by M. Brodmann PDF
- Proc. Amer. Math. Soc. 74 (1979), 16-18 Request permission
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 $A(n)$.References
- L. J. Ratliff Jr., On prime divisors of $I^{n},$ $n$ large, Michigan Math. J. 23 (1976), no.Β 4, 337β352 (1977). MR 457421
- D. Rees, Valuations associated with ideals, Proc. London Math. Soc. (3) 6 (1956), 161β174. MR 77513, DOI 10.1112/plms/s3-6.2.161
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 74 (1979), 16-18
- MSC: Primary 13E05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0521865-8
- MathSciNet review: 521865