Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin - Archive ouverte HAL Access content directly
Journal Articles Journal of Algebra Year : 2006

Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin

Guillaume Rond

Abstract

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 $X_1X_2-X_3X_4$, 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.

Dates and versions

hal-00125565 , version 1 (21-01-2007)

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Guillaume Rond. Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin. Journal of Algebra, 2006, 299, pp.245-275. ⟨hal-00125565⟩
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