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arXiv · 1010.1062

A Less Restrictive Brian\c{c}on-Skoda Theorem with Coefficients

Ian M. Aberbach·Aline Hosry
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Abstract

The Brian\c{c}on-Skoda theorem in its many versions has been studied by algebraists for several decades. In this paper, under some assumptions on an F-rational local ring $(R,\m)$, and an ideal $I$ of $R$ of analytic spread $\ell$ and height $g < \ell$, we improve on two theorems by Aberbach and Huneke. Let $J$ be a reduction of $I$. We first give results on when the integral closure of $I^\ell$ is contained in the product $J I_{\ell-1}$, where $I_{\ell-1}$ is the intersection of the primary components of $I$ of height $\leq \ell-1$. In the case that $R$ is also Gorenstein, we give results on when the integral closure of $I^{\ell-1}$ is contained in $J$.

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BibTeXRIS

Ian M. Aberbach, Aline Hosry. 2010-10-06. A Less Restrictive Brian\c{c}on-Skoda Theorem with Coefficients. https://arxiv.org/abs/1010.1062

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