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

TL;DR

This paper studies how certain generalized Cohen-Macaulay modules over local rings behave under Foxby equivalence, showing invariance and properties transfer between classes.

Contribution

It demonstrates the invariance of generalized Cohen-Macaulay modules under Foxby equivalence and links surjective Buchsbaum properties through this correspondence.

Findings

Generalized Cohen-Macaulay modules are invariant under Foxby equivalence.

If C⊗_RM is surjective Buchsbaum, then M is also surjective Buchsbaum.

The paper establishes new connections between module classes via Foxby equivalence.

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.