Equivalent Characterizations Of The Injective Objects In The Category Of ?-Left R-Modules

In this paper,the concepts of category of ?-left R-modules are introduced,the characteristics of monomorphism and epimorphism are studied in category of ?-left R-modules,some equivalent characterizations of monomorphism and epimorphism in the category of ?-left R-modules are given.we introduce the concept of injective object in the category of ?-left R-modules,equivalent descriptions of an injective object in the category of ?-left R-modules is investigated,a product of a bunch of?-left R-modules is an injective object if and only if every one is an injective object,a ?-left R-modules is an injective object if and only if it is every cut sets is proved to be an injective object.