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

Let R be a ring,X a class of R-modules and n ≥ 1 an integer.We intro-duce the concepts of Gorenstein n-X-injective and n-X-flat modules via special finitely presented modules.Besides,we obtain some equivalent properties of these modules on n-X-coherent rings.Then we investigate the relations among Gorenstein n-X-injective,n-X-flat,injective and fiat modules on X-FC-rings (i.e.,self n-X-injective and n-X-coherent rings).Several known results are generalized to this new context.