On the structure of sequentially generalized Cohen–Macaulay modules
- Cuong, Nguyen Tu
- Cuong, Doan Trung
DOIAbstract
AbstractA 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⊂⋯⊂Mt=M such that dimM0<dimM1<⋯<dimMt and each Mi/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 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 [N.T. Cuong, D.T. Cuong, dd-Sequences and partial Euler–Poincaré characteristics of Koszul complex, J. Algebra Appl. 6 (2) (2007...
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