Integral closure of ideals in excellent local rings

2002/10/28 by Donatella Delfino, Irena Swanson
Mathematics · #math.AC #msc:13B22 #msc:13B40 #msc:13J10 #msc:14B12

paper · pdf

published as Journal of Algebra, 187 (1997), 422-445 · Theorem 2.7 in the published version is wrong (we thank Ray Heitmann for pointing it out). This is a corrected version (the main results still hold)

arxiv created 2002/10/28 · arxiv updated 2009/11/30

Abstract

Let R be an excellent local ring, m its maximal ideal and I an ideal. Then there exists a positive integer c such that for all integers n, the integral closure of (I + mⁿ) is contained in m^(n/c) + the integral closure of I. In the proof, a version of the linear Artin approximation theorem is proved.

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