Quasi-unmixedness and integral closure of Rees rings
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- by Peter G. Sawtelle PDF
- Proc. Amer. Math. Soc. 56 (1976), 95-98 Request permission
Abstract:
For certain Rees rings $\mathcal {R}$ of a local domain $R$, the quasi-unmixedness of $R$ is characterized in terms of a certain transform of $\mathcal {R}$ being contained in the integral closure of $\mathcal {R}$.References
- Masayoshi Nagata, On the chain problem of prime ideals, Nagoya Math. J. 10 (1956), 51–64. MR 78974
- 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, Lessons on rings, modules and multiplicities, Cambridge University Press, London, 1968. MR 0231816
- J. W. Petro, Some results on the asymptotic completion of an ideal, Proc. Amer. Math. Soc. 15 (1964), 519–524. MR 162814, DOI 10.1090/S0002-9939-1964-0162814-3
- Louis J. Ratliff Jr., On quasi-unmixed semi-local rings and the altitude formula, Amer. J. Math. 87 (1965), 278–284. MR 179199, DOI 10.2307/2373005
- Louis J. Ratliff Jr., Note on analytically unramified semi-local rings, Proc. Amer. Math. Soc. 17 (1966), 274–279. MR 186691, DOI 10.1090/S0002-9939-1966-0186691-1
- L. J. Ratliff Jr., On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals. I, Amer. J. Math. 91 (1969), 508–528. MR 246867, DOI 10.2307/2373524
- L. J. Ratliff Jr., On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals. II, Amer. J. Math. 92 (1970), 99–144. MR 265339, DOI 10.2307/2373501
- L. J. Ratliff Jr., On prime divisors of the integral closure of a principal ideal, J. Reine Angew. Math. 255 (1972), 210–220. MR 311638, DOI 10.1515/crll.1972.255.210
- Peter G. Sawtelle, Quasi-unmixed local rings and quasi-subspaces, Proc. Amer. Math. Soc. 38 (1973), 59–64. MR 327755, DOI 10.1090/S0002-9939-1973-0327755-2 —, Characterizations of unmixed and quasi-unmixed local domains, Ph.D. Dissertation, University of California at Riverside, Riverside, Calif., 1971.
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0120249
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 95-98
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399073-0
- MathSciNet review: 0399073