On the Structure of Sequentially Generalized Cohen-Macaulay Modules

2007/01/25 by Nguyen Tu Cuong, Cuong, Nguyen Tu, Đoàn Trung Cường +2 · 1 citation
Computer Science · Mathematics · #13D45 #13H10 #13H15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13D45 #msc:13H10 #msc:13H15

paper · pdf · doi:10.48550/arxiv.math/0701729

28 pages

arxiv created 2007/01/25 · openalex publication_date 2007/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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: M₀⊂ M₁⊂ ... ⊂ M_t=M such that dim M₀<dim M₁< >... <dim M_t and each M_i/M_i-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 cohomology modules, theory of multiplicity and in terms of systems of parameters are given. We also show that the notion of dd-sequences defined in \citecc is an important tool for studying this class of modules.

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