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

2020/10/13 by Kosar Abolfath Beigi, Beigi, Kosar Abolfath, Kamran Divaani-Aazar +3
Mathematics · #13C14 #13D05 #13D45 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2010.06546

openalex publication_date 2020/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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