Linkage of modules and the Serre conditions

TL;DR

This paper explores how Serre conditions relate to linked modules over semiperfect Noetherian rings, showing that Cohen-Macaulayness can be preserved through linkage under certain conditions.

Contribution

It establishes a connection between Serre conditions and cohomology vanishing for linked modules, and demonstrates Cohen-Macaulayness preservation under linkage.

Findings

Serre condition $(S_n)$ relates to cohomology vanishing in linked modules.

Cohen-Macaulayness is preserved under certain linkage conditions.

Provides conditions under which linkage preserves desirable module properties.

Abstract

Let $R$ be semiperfect commutative Noetherian ring and $C$ be a semidualizing $R$--module. The connection of the Serre condition $(S_n)$ on a horizontally linked $R$-module of finite $\gc$-dimension with the vanishing of certain cohomology modules of its linked module is discussed. As a consequence, it is shown that under some conditions Cohen-Macaulayness is preserved under horizontally linkage.