Abstract: With methods of homological algebra, some properties of Ding-projective modules with respect to a semidualizing module C are investigated, and relationships between related classes of modules are given. It is proved that PC(R) is an injective cogenerator of DPC(R), where DPC(R) denotes the class of all DC-projective R-modules, and PC(R) denotes the class of all R-modules CRP with P projective module.

Key words: D_C-projective modules, semidualizing, injective cogenerator