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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A theorem of Briançon-Skoda type
for regular local rings containing a field


Authors: Ian M. Aberbach and Craig Huneke
Journal: Proc. Amer. Math. Soc. 124 (1996), 707-713
MSC (1991): Primary 13H05; Secondary 13A35, 13B22
MathSciNet review: 1301483
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $(R,m)$ be a regular local ring containing a field. We give a refinement of the Briançon-Skoda theorem showing that if $J$ is a minimal reduction of $I$ where $I$ is $m$-primary, then $\overline{I^{d+w}} \subseteq J^{w+1}\mathfrak{a}$ where $d = \dim R$ and $\mathfrak{a}$ is the largest ideal such that $\mathfrak{a} J = \mathfrak{a} I$. The proof uses tight closure in characteristic $p$ and reduction to characteristic $p$ for rings containing the rationals.


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Additional Information

Ian M. Aberbach
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: aberbach@msindy8.cs.missouri.edu

Craig Huneke
Affiliation: Department of Mathematics, Purdue University, W. Lafayette, Indiana 47907
Email: huneke@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03058-4
PII: S 0002-9939(96)03058-4
Keywords: Briancon-Skoda theorems, integral closure, tight closure
Received by editor(s): June 21, 1994
Received by editor(s) in revised form: September 7, 1994
Additional Notes: Both authors were partially supported by the National Science Foundation.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society