2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65461Let 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 + m^n) is contained in m^(n/c) + the integral closure of I. In the proof, a version of the linear Artin approximation theorem is proved.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)Commutative Algebra13B22; 13B40; 13J10; 14B12text