Gorenstein n-X -Injective and n - X-Flat Modules with Respect to a Special Finitely Presented Module

Let [Formula: see text] be a ring, class of text]-modules and an integer. We introduce the concepts Gorenstein text]-[Formula: text]-injective text]-flat modules via special finitely presented modules. Besides, we obtain some equivalent properties these on text]-coherent rings. Then investigate relations among text]-injective, text]-flat, injective flat text]-rings (i.e., self rings). Several known results are generalized to this new context.