On the Structure of Sequentially Generalized Cohen-Macaulay Modules

Details On the Structure of Sequentially Generalized Cohen-Macaulay Modules On the Structure of Sequentially Generalized Cohen-Macaulay Modules

2007-01-25

arxiv.org/abs/math/0701729v1

Mathematics

Commutative Algebra

28 pages

Scientific paper

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 $M$: $M_0\subset M_1\subset ... \subset M_t=M$ such that $\dim M_0<\dim M_1< >... <\dim M_t$ 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 \cite{cc} is an important tool for studying this class of modules.

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