On the uniform bound of the index of reducibility of parameter ideals of a module whose polynomial type is at most one

Abstract

Abstract. Let (R, m) be a Noetherian local ring, M a finitely generated R-module. The aim of this paper is to prove a uniform formula for the index of reducibility of parameter ideals of M provided the polynomial type of M is at most one. ... Keywords. The index of reducibility, The polynomial type of a module, Local cohomology. ... 1. Introduction. Throughout this paper, let (R, m) be a Notherian local ring, M a finitely generated R-module of dimension d. Let x = x1,...,xd be a system of parameters of M and q = (x1,...,xd). Let n = (n1,...,nd) be a d-tuple of positive integers ...