On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence
K Abolfath Beigi, K Divaani-Aazar, M Tousi - Czechoslovak Mathematical …, 2022 - Springer
K Abolfath Beigi, K Divaani-Aazar, M Tousi
Czechoslovak Mathematical Journal, 2022•SpringerLet 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.
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.
Abstract
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.
Springer
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