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

DOI:
https://doi.org/10.1090/S0002-9939-96-03058-4

MathSciNet review:
1301483

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Abstract | References | Similar Articles | Additional Information

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 where and is the largest ideal such that . The proof uses tight closure in characteristic and reduction to characteristic 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:
https://doi.org/10.1090/S0002-9939-96-03058-4

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