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

Authors:	Ian M Aberbach Craig Huneke

Institution:	Department of Mathematics, University of Missouri, Columbia, Missouri 65211 ; Department of Mathematics, Purdue University, W. Lafayette, Indiana 47907

Abstract:	Let be a regular local ring containing a field. We give a refinement of the Briançon-Skoda theorem showing that if is a minimal reduction of where is -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 and reduction to characteristic for rings containing the rationals.

Keywords:	Briancon-Skoda theorems integral closure tight closure

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