Asymptotic behaviour of good systems of parameters of sequentially generalized Cohen-Macaulay modules

Abstract

Let (R,$\mathfrak{m}$) be a commutative Noetherian local ring. A finitely generated R-module M is called sequentially generalized Cohen-Macaulay module if there is a filtration M₀ $\subseteq$ M₁ $\subseteq$ ··· $\subseteq$ M_t = M of submodules of M such that 0 = dim M₀ < dim M₁ < ··· < dim M_t and each M_i/M_i–1 is a generalized Cohen-Macaulay module. In this paper we study the asymptotic behavior of good systems of parameters, introduced in [N. T. Cuong, D. T. Cuong, On sequentially Cohen-Macaulay modules, Kodai Math. J. 30 (2007), 409-428], of sequentially generalized Cohen-Macaulay modules.