Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 989-1002, 2022

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

Kosar Abolfath Beigi, Kamran Divaani-Aazar, Massoud Tousi

Received June 22, 2021. Published online March 21, 2022.

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 $C\otimes_RM$ is surjective Buchsbaum, then $M$ is also surjective Buchsbaum.

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

Classification MSC: 13C14, 13D05, 13D45

DOI: 10.21136/CMJ.2022.0227-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Kosar Abolfath Beigi, Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, North Sheikh Bahaee St., 1993891176 Tehran, Iran, e-mail: kosarabolfath@gmail.com; Kamran Divaani-Aazar, Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran, e-mail: kdivaani@ipm.ir; Massoud Tousi, Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, P.O. Box 19395-5746, Tehran, Iran, e-mail: mtousi@ipm.ir

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