Notes on linkage of modules with respect to a semidualizing module

Abstract

In this paper we further develop the theory of linkage with respect to a semidualizing module C introduced in 2018 by Dibaei and Sadeghi. It is shown that under certain conditions a module of ${\mathrm{G}}_C$-dimension zero is horizontally linked with respect to C. Moreover, for a module which is horizontally linked with respect to C, the connections of its invariants reduced grade with respect to C and ${\mathrm{G}}_C$-dimension are discussed.

KEYWORD:

• Auslander class
• Bass class
• ${\mathrm{G}}_C$-dimension
• reduced grade
• linkage of modules
• semidualizing modules

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13C40
• 13D05
• 13D07
• Secondary: 13C14
• 13C15
• 13H10