Linkage of finite Gorenstein dimension modules

For a horizontally linked module, over a commutative semiperfect Noetherian ring R, the connections of its invariants reduced grade, Gorenstein dimension and depth are studied. It is shown that under certain conditions the depth of a horizontally linked module is equal to the reduced grade of its linked module. The connection of the Serre condition (Sn) on an R-module of finite Gorenstein dimension with the vanishing of the local cohomology groups of its linked module is discussed.