In this paper, we define modules with the properties (d-GSCE) and (d-GSCEE) by adapting Zöschinger’s modules with the properties (E) and (EE) and we investigate the structure of modules with these properties. It is shown that: (1) a module has the property (d-GSCEE) iff every submodule has the property (d-GSCE); (2) the property (d-GSCE) is inherited by direct summands; (3) for an R-module M over a d-V-ring, M has the property (d-GSCE) iff M is cofinitely injective; (4) if R is a d-semiperfect ring, then every left R-module has the property (d-GSCE).

d-supplement, d-semiperfect, cofinite extension.