| In this paper,we mainly investigate some properties of Gorenstein C-homologi-cal modules and Gorenstein C-homological dimensions of modules.Let C be an(R,S)-bimodule.Firstly,we investigate some properties and equivalent characteri-zations of Gorenstein C-projective module,and prove that the class of Gorenstein C-projective modules is AddR(C)-resolving when RC is E-self-orthogonal,self-small and Cs is(?)-faithful.On this basis,we define Gorenstein C-projective dimension of module,and give some equivalent characterizations of module with finite Goren-stein C-projective dimension,investigate the relations of Gorenstein C-projective dimension,GC-projective dimension and AddR(C)-projective dimension of module.Finally,the Foxby equivalence of Gorenstein C-homological modules are investigat-ed. |
