X-G_C-projective Mdules And Dimensions

Let X be a class contains all projective modules, and X is contained in Ac(R)-In this paper, we define X-Gc-projective modules. We mainly study projectively resolv-ing, stability and character dimensions of the class of these modules. First of all, we introduce some basic homological properties of X-Gc-projective modules. We prove that the class of X-Gc-projective modules is projectively resolving. Also the stabil-ity of the class of X-Gc-projective modules is investigated. Secondly, we introduce the notion of X-Gc-projective dimensions of modules and some equivalent charac-terizations of modules whose X-Gc-projective dimensions be finited are given.