On the structure of sequentially Cohen--Macaulay bigraded modules

Let \(K\) be a field and \(S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]\) be the standard bigraded polynomial ring over \(K\). In this paper, we explicitly describe the structure of finitely generated bigraded "sequentially Cohen--Macaulay" \(S\)-modules with respect to \(Q=(y_1,\ldots,y_n)\). Next...

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Bibliographic Details
Published in:arXiv.org 2015-10
Main Authors: Leila Parsaei Majd, Rahimi, Ahad
Format: Article
Language:English
Subjects:
Homology
Modules
Polynomials
Rings (mathematics)
Online Access:Get full text
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Summary:Let \(K\) be a field and \(S=K[x_1,\ldots,x_m, y_1,\ldots,y_n]\) be the standard bigraded polynomial ring over \(K\). In this paper, we explicitly describe the structure of finitely generated bigraded "sequentially Cohen--Macaulay" \(S\)-modules with respect to \(Q=(y_1,\ldots,y_n)\). Next, we give a characterization of sequentially Cohen--Macaulay modules with respect to \(Q\) in terms of local cohomology modules. Cohen--Macaulay modules that are sequentially Cohen--Macaulay with respect to \(Q\) are considered.
ISSN:2331-8422