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Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences

Katzman, Mordechai and Sharp, Rodney Y. (2005) Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences. Journal of Algebra, 295 (1). pp. 231-246. ISSN 0021-8693

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Abstract

This paper is concerned with ideals in a commutative Noetherian ring R of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of R generated by regular sequences exhibit a desirable type of 'uniform' behaviour. The principal technical tool used is a result, proved by R. Hartshorne and R. Speiser in the case where R is local and contains its residue field which is perfect, and subsequently extended to all local rings of prime characteristic by G. Lyubeznik, about a left module over the skew polynomial ring R[x, f] (associated to R and the Frobenius homomorphism f, in the indeterminate x) that is both x-torsion and Artinian over R. (c) 2005 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; tight closure; (Weak) test element; Artinian module; skew polynomial ring; regular sequence; 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 14:33
Last Modified: 08 Feb 2013 16:59
Published Version: http://dx.doi.org/10.1016/j.jalgebra.2005.01.025
Status: Published
Publisher: Elsevier
Identification Number: 10.1016/j.jalgebra.2005.01.025
URI: http://eprints.whiterose.ac.uk/id/eprint/10173

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