A uniform bound of reducibility index of good parameter ideals for certain class of modules

Abstract

Let (R,m) be a Noetherian local ring and M a finitely generated R-module. The invariants p(M) and sp(M) of M were introduced in [3] and [17] in order to measure the non-Cohen–Macaulayness and the non-sequential-Cohen–Macaulayness of M, respectively. Let M=D0⊃D1⊃…⊃Dk be the filtration of M such that Di is the largest submodule of M of dimension less than dim⁡Di−1 for all i≤k and p(Dk)≤1. In this paper we prove that if sp(M)≤1, then there exists a constant c such that irM(qM)≤c for all good parameter ideals q of M with respect to this filtration. Here irM(qM) is the reducibility index of q on M. This is an extension of the main results of [19], [20], [24].