Vol. 294, No. 2, 2018

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Linkage of modules with respect to a semidualizing module

Mohammad T. Dibaei and Arash Sadeghi

Vol. 294 (2018), No. 2, 307–328
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 (Sn) 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
Authors
Mohammad T. Dibaei
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
Tehran
Iran
Faculty of Mathematical and Computer Sciences
Kharazmi University
Tehran
Iran
Arash Sadeghi
School of Mathematics
Institute for Research in Fundamental Sciences (IPM)
Tehran
Iran