Linkage of modules and the Serre conditions

Let R be semiperfect commutative Noetherian ring and C be a semidualizing R  -module. The connection of the Serre condition (Sn)(Sn) on a horizontally linked R  -module of finite GCGC-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 horizontal linkage.