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Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings

Huneke, Craig, Katzman, Mordechai, Sharp, Rodney Y. and Yao, Yongwei (2006) Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings. Journal of Algebra, 305 (1). pp. 516-539. ISSN 0021-8693

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This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal a of R, there is a power Q of p, depending on a, such that the Qth Frobenius power of the Frobenius closure of a is equal to the Qth Frobenius power of a. The paper addresses the question as to whether there exists a uniform Q(0) which 'works' in this context for all parameter ideals of R simultaneously. In a recent paper, Katzman and Sharp proved that there does exists such a uniform Q(0) when R is Cohen-Macaulay. The purpose of this paper is to show that such a uniform Q(0) exists when R is a generalized Cohen-Macaulay local ring. A variety of concepts and techniques from commutative algebra are used, including unconditioned strong d-sequences, cohomological annihilators, modules of generalized fractions, and the Hartshome-Speiser-Lyubeznik Theorem employed by Katzman and Sharp in the Cohen-Macaulay case. (c) 2006 Elsevier Inc. All rights reserved.

Item Type: Article
Copyright, Publisher and Additional Information: © 2006 Elsevier. This is an author produced version of a paper subsequently published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: commutative Noetherian ring; prime characteristic; Frobenius homomorphism; Frobenius closure; generalized Cohen-Macaulay local ring; unconditioned strong d-sequence; filter-regular sequence; Artinian module; Frobenius skew polynomial ring; local cohomology module
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 18 Nov 2009 12:05
Last Modified: 08 Feb 2013 16:59
Published Version: http://dx.doi.org/10.1016/j.jalgebra.2006.06.036
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.jalgebra.2006.06.036
URI: http://eprints.whiterose.ac.uk/id/eprint/10176

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