Note on asymptotic prime divisors, analytic spreads and the altitude formula
HTML articles powered by AMS MathViewer
- by L. J. Ratliff
- Proc. Amer. Math. Soc. 82 (1981), 1-6
- DOI: https://doi.org/10.1090/S0002-9939-1981-0603590-7
- PDF | Request permission
Abstract:
The main result gives several characterizations of Noetherian domains that satisfy the altitude formula in terms of analytic spreads and 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
- Stephen McAdam and Paul Eakin, The asymptotic $\textrm {Ass}$, J. Algebra 61 (1979), no.Β 1, 71β81. MR 554852, DOI 10.1016/0021-8693(79)90306-5
- Stephen McAdam, Asymptotic prime divisors and analytic spreads, Proc. Amer. Math. Soc. 80 (1980), no.Β 4, 555β559. MR 587926, DOI 10.1090/S0002-9939-1980-0587926-0
- 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
- D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145β158. MR 59889, DOI 10.1017/s0305004100029194
- L. J. Ratliff Jr., Locally quasi-unmixed Noetherian rings and ideals of the principal class, Pacific J. Math. 52 (1974), 185β205. MR 352085
- L. J. Ratliff Jr., On prime divisors of $I^{n},$ $n$ large, Michigan Math. J. 23 (1976), no.Β 4, 337β352 (1977). MR 457421
- L. J. Ratliff Jr., Two theorems on the prime divisors of zeros in completions of local domains, Pacific J. Math. 81 (1979), no.Β 2, 537β545. MR 547619
- Motoyoshi Sakuma and Hiroshi Okuyama, On a criterion for analytically unramification of a local ring, J. Gakugei Tokushima Univ. 15 (1966), 36β38. MR 200290
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 1-6
- MSC: Primary 13A17; Secondary 13E05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0603590-7
- MathSciNet review: 603590