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Tightly closed ideals of small type


Author: Adela Vraciu
Journal: Proc. Amer. Math. Soc. 132 (2004), 341-346
MSC (2000): Primary 13A35
DOI: https://doi.org/10.1090/S0002-9939-03-07085-0
Published electronically: September 5, 2003
MathSciNet review: 2022354
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Abstract: We study the smallest possible type of tightly closed ideals that are cofinal with the powers of the maximal ideal; this numerical invariant yields information about the tight closure of arbitrary ideals in the ring.


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  • [HH1] M. Hochster and C. Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31-116. MR 91g:13010
  • [HH2] M. Hochster and C. Huneke, F-regularity, test elements, and smooth base change, Trans. Amer. Math. Soc. 346 (1994), 1-62. MR 95d:13007
  • [HH3] M. Hochster and C. Huneke, Tight closure of parameter ideals and splitting in module-finite extensions, J. Algebraic Geom. 3 (1994), 599-670. MR 95k:13002
  • [HHV] M. Hochster, C. Huneke, and A. Vraciu, Big ideals, in preparation.
  • [Hu] C. Huneke, Tight closure and strong test ideals, J. Pure Applied Algebra 122 (1997), 243-250. MR 98g:13003
  • [Vr] A. Vraciu, Strong test ideals, J. Pure Applied Algebra 167 (2002), 361-373. MR 2003a:13004
  • [Wa] K.-i. Watanabe, Study of F-purity in dimension two, Algebraic Geometry and Commutative Algebra in honor of Masayoshi Nagata, vol. II, Kinokuniya, Tokyo, 1988, 791-800. MR 90b:14005

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Additional Information

Adela Vraciu
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Address at time of publication: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email: avraciu@math.ukans.edu, vraciu@math.sc.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07085-0
Keywords: Tight closure, type
Received by editor(s): July 8, 2002
Received by editor(s) in revised form: October 9, 2002
Published electronically: September 5, 2003
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2003 American Mathematical Society

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