On the structure of sequentially Cohen-Macaulay bigraded modules

Czechoslovak Mathematical Journal

Leila Parsaei Majd¹  Ahad Rahimi² 

[1] Department of Mathematics, Faculty of Science, Razi University, Baghe Abrisham, Kermanshah, Iran, and Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, P. O. Box: 16785-136, Tehran, Iran;Department of Mathematics, Faculty of Science, Razi University, Baghe Abrisham, Kermanshah, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box: 19395-5746, Tehran, Iran

关键词: dimension filtration;    sequentially Cohen-Macaulay filtration;    cohomological dimension;    bigraded module;    Cohen-Macaulay module;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

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.

【 授权许可】

Unknown