Two applications of asymptotic prime divisors
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- by Stephen McAdam
- Proc. Amer. Math. Soc. 84 (1982), 179-180
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637164-X
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Abstract:
Some recent interest has focused on the set of prime divisors of large powers of an ideal in a Noetherian ring. This note presents two results whose proofs appear to depend on knowledge of such asymptotic prime divisors.References
- M. Brodmann, Asymptotic stability of $\textrm {Ass}(M/I^{n}M)$, Proc. Amer. Math. Soc. 74 (1979), no.Β 1, 16β18. MR 521865, DOI 10.1090/S0002-9939-1979-0521865-8
- Irving Kaplansky, Commutative rings, Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
- Stephen McAdam, Asymptotic prime divisors and going down, Pacific J. Math. 91 (1980), no.Β 1, 179β186. MR 612897
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
- L. J. Ratliff Jr., On prime divisors of $I^{n},$ $n$ large, Michigan Math. J. 23 (1976), no.Β 4, 337β352 (1977). MR 457421
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 179-180
- MSC: Primary 13B20; Secondary 13H10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0637164-X
- MathSciNet review: 637164