Analytic spread of nitrations, asymptotic nature and some stability properties

Abstract

hlany concepts of analytic spread for filtrations exist in the current literature. As far as we know, none of t,hem is explicitly of asymptotic nature. Here we give a definition of analytic spread for filtr;lth~s whir11 is shoWu to be of asyrnptotic nature. 011 the other hand, it is known that, in a noetherian local ring, the analytic spread of ideals is invariant under the integral closure operation. In this paper we investigate too t,he behaviour of the analytic spread of a filtration f under some closure operations, the analytic spread of f = (I,)