Commutative Ring Theory

23 Some Aspects of the Asymptotic Theory of Ideals. Generalization to Filtrations

DAOUD A SANGARE Département de Mathématiques, FAST, Université d’Abidjan, 22 B. P. 582, Abidjan, Cote d’Ivoire

Introduction

The asymptotic theory of ideals originated with the paper “Some asymptotic properties of powers of ideals “by Pierre SAMUEL [13]. This theory is based on the fact that in a nœtherian ring, large powers of an ideal are well behaved in some sense. It gives useful tools in commutative algebra and also in algebraic geometry. This theory has been developed at the beginning by D. Rees and M. Nagata and more recently by many other authors. It deals with topics like Samuel numbers of two ideals, homogeneous pseudo valuations, Rees valuation theorem, ...