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Keywords:
Auslander class; Bass class; Buchsbaum module; dualizing module; generalized Cohen-Macaulay module; local cohomology; semidualizing module; surjective Buchsbaum module
Auslander class; Bass class; Buchsbaum module; dualizing module; generalized Cohen-Macaulay module; local cohomology; semidualizing module; surjective Buchsbaum module
Summary:
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
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