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Tightly closed ideals of small type

Author(s): Adela Vraciu
Journal: Proc. Amer. Math. Soc. 132 (2004), 341-346.
MSC (2000): Primary 13A35
Posted: September 5, 2003
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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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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

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M. Hochster, C. Huneke, and A. Vraciu, Big ideals, in preparation.

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A. Vraciu, Strong test ideals, J. Pure Applied Algebra 167 (2002), 361-373. MR 2003a:13004

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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: 10.1090/S0002-9939-03-07085-0
PII: S 0002-9939(03)07085-0
Keywords: Tight closure, type
Received by editor(s): July 8, 2002
Received by editor(s) in revised form: October 9, 2002
Posted: September 5, 2003
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2003, American Mathematical Society

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