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Quasi-unmixedness and integral closure of Rees rings


Author: Peter G. Sawtelle
Journal: Proc. Amer. Math. Soc. 56 (1976), 95-98
DOI: https://doi.org/10.1090/S0002-9939-1976-0399073-0
MathSciNet review: 0399073
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Abstract | References | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] M. Nagata, On the chain problem of prime ideals, Nagoya Math. J. 10 (1956), 51-64. MR 18, 8. MR 0078974 (18:8e)
  • [2] -, Local rings, Interscience Tracts in Pure and Appl. Math., no. 13, Interscience, New York, 1962. MR 27 #5790. MR 0155856 (27:5790)
  • [3] D. G. Northcott, Lessons on rings, modules, and multiplicities, Cambridge Univ. Press, London, 1968. MR 38 #144. MR 0231816 (38:144)
  • [4] J. W. Petro, Some results on the asymptotic completion of an ideal, Proc. Amer. Math. Soc. 15 (1964), 519-524. MR 29 #118. MR 0162814 (29:118)
  • [5] L. J. Ratliff, Jr., On quasi-unmixed semi-local rings and the altitude formula, Amer. J. Math. 87(1965), 278-284. MR 31 #3448. MR 0179199 (31:3448)
  • [6] -, Note on analytically unramified semi-local rings, Proc. Amer. Math. Soc. 17 (1966), 274-279. MR 32 #4149. MR 0186691 (32:4149)
  • [7] -, On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals. I, Amer. J. Math. 91 (1969), 508-528. MR 40 #136. MR 0246867 (40:136)
  • [8] -, On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals. II, Amer. J. Math. 92 (1970), 99-144. MR 42 #249. MR 0265339 (42:249)
  • [9] -, On prime divisors of the integral closure of a principal ideal, J. Reine Angew. Math. 255 (1972), 210-220. MR 47 #200. MR 0311638 (47:200)
  • [10] Peter G. Sawtelle, Quasi-unmixed local rings and quasi-subspaces, Proc. Amer. Math. Soc. 38 (1973), 59-64. MR 48 #6097. MR 0327755 (48:6097)
  • [11] -, Characterizations of unmixed and quasi-unmixed local domains, Ph.D. Dissertation, University of California at Riverside, Riverside, Calif., 1971.
  • [12] O. Zariski and P. Samuel, Commutative algebra. Vol. II, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #11006. MR 0120249 (22:11006)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399073-0
Keywords: Local ring, quasi-unmixed, integral closure, Rees ring
Article copyright: © Copyright 1976 American Mathematical Society

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