#### Vol. 294, No. 2, 2018

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Linkage of modules with respect to a semidualizing module

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 $\left({S}_{n}\right)$ 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
Primary: 13C40
Secondary: 13D05