Divisions selon les puissances fractionnaires d'un idéal engendré par une suite régulière dans l'anneau des germes à l'origine de fonctions holomorphes sur [formula omitted

Abstract

Consider the ring of germs of analytic functions at the origin of C 2 . Let I be an ideal of this ring, and let us denote by I , the integral closure of this ideal. J. Lipman and B. Teissier proved that the following formula: I n+1 = I·I n , holds for every integer n. In this paper, we discuss, under certain condition over I, of a similar formula for the fractional powers of I.