A measure of non-sequential Cohen–Macaulayness of finitely generated modules

Let M be a finitely generated module over a Noetherian local ring R. In this paper we introduce the notion of sequential polynomial type of M  , which is denoted by sp(M)sp(M), in order to measure how far M   is different from the sequential Cohen–Macaulayness. We study the sequential polynomial type under localization and mm-adic completion. We investigate an ascent–descent property of sequential polynomial type between M   and M/xMM/xM for certain parameter x of M. When R   is a quotient of a Gorenstein local ring, we describe sp(M)sp(M) in term of the deficiency modules of M.