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On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 989-1002
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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 $C\otimes _RM$ is surjective Buchsbaum, then $M$ is also surjective \hbox {Buchsbaum}.\looseness +1
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 $C\otimes _RM$ is surjective Buchsbaum, then $M$ is also surjective \hbox {Buchsbaum}.\looseness +1
DOI : 10.21136/CMJ.2022.0227-21
Classification : 13C14, 13D05, 13D45
Keywords: Auslander class; Bass class; Buchsbaum module; dualizing module; generalized Cohen-Macaulay module; local cohomology; semidualizing module; surjective Buchsbaum module 
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     title = {On the invariance of certain types of generalized {Cohen-Macaulay} modules under {Foxby} equivalence},
     journal = {Czechoslovak Mathematical Journal},
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     year = {2022},
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Abolfath Beigi, Kosar; Divaani-Aazar, Kamran; Tousi, Massoud. On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 4, pp. 989-1002. doi: 10.21136/CMJ.2022.0227-21

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