On the sequential polynomial type of modules

Abstract

Let M be a finitely generated module over a Noetherian local ring R. The sequential polynomial type sp(M) of M was recently introduced by Nhan, Dung and Chau, which measures how far the module M is from the class of sequentially Cohen–Macaulay modules. The present paper purposes to give a parametric characterization for M to have sp(M) ≤ s, where s ≥ −1 is an integer. We also study the sequential polynomial type of certain specific rings and modules. As an application, we give an inequality between sp(S) and sp(S^G), where S is a Noetherian local ring and G is a finite subgroup of AutS such that the order of G is invertible in S.