X-Gorenstein Projective and Y-Gorenstein Injective Modules

Let X be a class of right R-modules that contains all projective right R-modules. The notion of X-Gorenstein projective modules was intro- duced by D. Bennis and K. Ouarghi (X-Gorenstein projective mod- ules, International Mathematical Forum 5(10), 487-491, 2010). In this paper, we introduce Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules, where Y is a class of right R-modules that contains all injective right R-modules. We show that the princi- pal results on Gorenstein modules remain true for X-Gorenstein pro- jective right R-modules, Y-Gorenstein injective right R-modules and Y-Gorenstein flat left R-modules.