Generalization of injective modules

There are important applications of injective modules in the module theory. Theory of injective modules goes back to years of 1950. In this thesis, injective modules and their generalizations have been studied. For this fact, definitions of some different injective modules and their basic properties are given. Definitions of A-injective and A-essential injective module, principally injective module, quasi-injective and pseudo-injective module have been reviewed. Definitions of f -injective module, small PP-M-injective module and small PPQ-injective module, SP-M-injective and relative injective module have been studied. Finally, we gave relations of the injective modules which they mentioned in this study.