Artin-Rees Lemma, Izumi theorem and Artin function (Q2497456)

From the author's abstract: The author interprets the Artin-Rees lemma and the Izumi theorem in terms of Artin function and he obtains a stable version of the Artin-Rees lemma. He presents different applications of these interpretations. First he shows 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 he proves that the Artin functions of a class of polynomials are bounded by affine functions and he uses this to compute approximated integral closure of ideals.