A theory of multiplicity for multiplictive filtrations.

Abstract

A result in the theory of commutative rings [4], (21. 1) states that for a 0-dimensional ideal α in a noetherian ring A with identity and a finitely generated ^4-module M, the (cumulative) Hubert function L A (M/a n M) is a polynomial with rational coefficients for all sufficiently large n. This polynomial has degree at most s, the altitude of the ideal a. The multiplicity of M with respect to a is s! times the coefficient of the term of degree s and is frequently expressed by the limit formula of Samuel *) This research represents a portion of the author's doctoral dissertation at Western Michigan University.