Y-Gorenstein Cotorsion Modules

Let R be an associative ring with identity,and Y be a class of right R-modules,which contains all injective right R-modules.In this paper,we introduce the definition of Y-Gorenstein cotorsion modules,which is a generalization of cotorsion and Gorenstein cotorsion modules.We discuss the relationship between Gorenstein cotorsion,weakly Gorenstein cotorsion and Y-Gorenstein cotorsion modules.We investigate properties and characterizations of Y-Gorenstein cotorsion modules.