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 $(S_n)$ on a horizontally linked $R$-module of finite $\text{gc}$-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 horizontally linkage.