Some Studies On Pseudo-injective Modules

In this paper,the properties and applications of pseudo injective modules which is an important generalization of injective modules are further discussed.In chapter 1,we will introduce some prediminary knowledge,review the definitions of some important modules and rings,and describe the properties of some special rings in terms of injective modules.In chapter 2,some perfect properties of pseudo injective modules will be included.For example,the pseudo injectivity of the modules which are the submodules of pseudo injective modules;the relationship between quasi injective modules and pseudo injective modules;Pseudo injective precovers,etc.In chapter 3,some spcical rings are described in terms of pseudo injective modules. For example,R is left hereditary ring if and only if each factor module of every injective module is pseudo injective module;R is semisimple ring if and only if each left R-module is pseudo injective module;R is V ring if and only if each finitely cogenerated left R-module is pseudo injective module,etc.