On Weakly Gorenstein FP-injective Modules

Let A be an Abelian category with enough projective objects and enough injective objects,and let (?) =(F,C)be a complete hereditary cotorsion pair in .In this paper,we define the notions of Gorenstein objects related to this cotorsion pair: (?)Gorenstein projective objects and (?)-Gorenstein injective objects,and discuss some elementary properties of these objects.Then applying this idea to the cotorison pair consisting of the class of FP-projective modules and the class FP-projective modules over a right coherent ring,we give the notion of weakly Gorenstein FP-injective modules,and prove some properties of weakly Gorenstein FP-injective modules.We also use weakly Gorenstein FP-injective modules to characterize IF rings.