On the structure of sequentially generalized Cohen-Macaulay modules

JOURNAL OF ALGEBRA

卷:317

Article

Cuong, Nguyen Tu¹  Cuong, Doan Trung¹ 

[1] Inst Math, Hanoi 10307, Vietnam

关键词: good system of parameters;    generalized Cohen-Macaulay filtration;    sequentially generalized Cohen-Macaulay module;    local cohomology module;   

DOI  :  10.1016/j.jalgebra.2007.06.026

来源: Elsevier

【 摘 要 】

A finitely generated module M over a local ring is called a sequentially generalized Cohen-Macaulay module if there is a filtration of submodules of M : M-0 subset of M-1 subset of ... subset of M-t = M such that dim M-0 < dim M-1 < ... < dim M-t and each M-i/Mi-1 is generalized Cohen-Macaulay. The aim of this paper is to study the structure of this class of modules. Many basic properties of these modules are presented and various characterizations of sequentially generalized Cohen-Macaulay property by using local cohomoloay modules, theory of multiplicity and in terms of systems of parameters are given. We also show that the notion of dd-sequences defined in [N.T. Cuong, D.T. Cuong, dd-Sequences and partial Euler-Poincare characteristics of Koszul complex, J. Algebra Appl. 6 (2) (2007) 207-231] is an important tool for studying this class of modules. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free