Characterization of injective modules

Injective modules take important place in the development of module theory. The theory of injective modules being developed by different definitions and thus researchers make a lot of generalizations of injective modules. In this thesis, we study some different generalizations of injective modules in the sense of characterizations. Therefore A-injective, principally injective, quasi-injective, pseudo-injective, f -injective, PP-M-injective, small PPQ-injective and SP-M-injective modules has been studied and equivalent conditions has been examined for characterizations. Finally, the relations of this injective modules has been given for further characterizations.