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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Briançon-Skoda theorem and coefficient ideals for non-$\mathfrak {m}$-primary ideals
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by Ian M. Aberbach and Aline Hosry PDF
Proc. Amer. Math. Soc. 139 (2011), 3903-3907 Request permission

Abstract:

We generalize a Briançon-Skoda type theorem first studied by Aberbach and Huneke. With some conditions on a regular local ring $(R,\mathfrak {m})$ containing a field, and an ideal $I$ of $R$ with analytic spread $\ell$ and a minimal reduction $J$, we prove that for all $w \geq -1$, $\overline {I^{\ell +w}} \subseteq J^{w+1} \mathfrak {a} (I,J),$ where $\mathfrak {a}(I,J)$ is the coefficient ideal of $I$ relative to $J$, i.e. the largest ideal $\mathfrak {b}$ such that $I\mathfrak {b}=J\mathfrak {b}$. Previously, this result was known only for $\mathfrak {m}$-primary ideals.
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Additional Information
  • Ian M. Aberbach
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • MR Author ID: 314830
  • Email: aberbachi@missouri.edu
  • Aline Hosry
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • Email: aline.hosry@mizzou.edu
  • Received by editor(s): October 5, 2010
  • Published electronically: March 28, 2011
  • Communicated by: Irena Peeva
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3903-3907
  • MSC (2010): Primary 13A35, 13H05
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10871-2
  • MathSciNet review: 2823036