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 C2

Consider the ring of germs of analytic functions at the origin of $\text{C}{}^2$. Let I be an ideal of this ring, and let us denote by $\text{I}$, the integral closure of this ideal. J. Lipman and B. Teissier proved that the following formula: $\text{I}{}^{\mathrm{n+1}}\text{=}\text{I}\text{·I}{}^{\mathrm{n}}$, 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.