Lemme d ’ Artin – Rees , théorème d ’ Izumi et fonction de Artin Guillaume Rond
نویسندگان
چکیده
We interpret the Artin–Rees lemma and the Izumi theorem in term of Artin function and we obtain a stable version of the Artin–Rees lemma. We present different applications of these interpretations. First we show that the Artin function of X1X2 −X3X4, as a polynomial in the ring of power series in more than three variables, is not bounded by an affine function. Then we prove that the Artin functions of a class of polynomials are bounded by affine functions and we use this to compute approximated integral closures of ideals. 2005 Elsevier Inc. All rights reserved. Mots-clés : Théorème d’approximation forte de Artin ; Fonction de Artin ; Lemme d’Artin–Rees ; Théorème d’Izumi ; Clôture intégrale d’idéaux
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