Linkage of modules with respect to a semidualizing module

Mohammad T. Dibaei and Arash Sadeghi

Vol. 294 (2018), No. 2, 307–328

DOI: 10.2140/pjm.2018.294.307

Abstract

The notion of linkage with respect to a semidualizing module is introduced. This notion enables us to study the theory of linkage for modules in the Bass class with respect to a semidualizing module. It is shown that over a Cohen–Macaulay local ring with canonical module, every Cohen–Macaulay module of finite Gorenstein injective dimension is linked with respect to the canonical module. For a linked module $M$ with respect to a semidualizing module, the connection between the Serre condition $\left(S_n\right)$ on $M$ and the vanishing of certain local cohomology modules of its linked module is discussed.

Keywords

linkage of modules, Auslander classes, Bass classes, semidualizing modules, $\mathsf{G}_C$-dimensions

Mathematical Subject Classification 2010

Primary: 13C40

Secondary: 13D05

Milestones

Received: 1 July 2017

Revised: 26 November 2017

Accepted: 29 November 2017

Published: 20 February 2018