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

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- by Ian M. Aberbach and Craig Huneke PDF
- Proc. Amer. Math. Soc.
**124**(1996), 707-713 Request permission

## 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.## References

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## Additional Information

**Ian M. Aberbach**- Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
- MR Author ID: 314830
- Email: aberbach@msindy8.cs.missouri.edu
**Craig Huneke**- Affiliation: Department of Mathematics, Purdue University, W. Lafayette, Indiana 47907
- MR Author ID: 89875
- Email: huneke@math.purdue.edu
- 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
- © Copyright 1996 American Mathematical Society
- 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