On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence

被引：0
|
作者：
Kosar Abolfath Beigi
Kamran Divaani-Aazar
Massoud Tousi
机构：
[1] Alzahra University,Department of Mathematics, Faculty of Mathematical Sciences
[2] Institute for Research in Fundamental Sciences (IPM),School of Mathematics
[3] Shahid Beheshti University,Department of Mathematics, Faculty of Mathematical Sciences
来源：
Czechoslovak Mathematical Journal | 2022年 / 72卷
关键词：
Auslander class; Bass class; Buchsbaum module; dualizing module; generalized Cohen-Macaulay module; local cohomology; semidualizing module; surjective Buchsbaum module; 13C14; 13D05; 13D45;
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摘要：
Let R be a local ring and C a semidualizing module of R. We investigate the behavior of certain classes of generalized Cohen-Macaulay R-modules under the Foxby equivalence between the Auslander and Bass classes with respect to C. In particular, we show that generalized Cohen-Macaulay R-modules are invariant under this equivalence and if M is a finitely generated R-module in the Auslander class with respect to C such that C ⊗RM is surjective Buchsbaum, then M is also surjective Buchsbaum.
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页码：989 / 1002
页数：13
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