Research On Two Kinds Of Graded Gorenstein Homology Modules

In this thesis,we introduce and study the homological properties of two classes of graded Gorenstein modules.The thesis is divided into three chapters.The first chapter gives some preliminaries needed in this thesis.In the second chapter,we study Gorenstein FP-gr-injective modules,some homological properties of Gorenstein FP-gr-injective modules are given on graded ring R.Then we discuss the relations between Gorenstein FP-gr-injective modules and Gorenstein gr-flat modules,and some known classes of graded rings are characterized in terms of Gorenstein FP-gr-injective modules.Also,we investigate the connections between the graded and the ungraded Gorenstein FP-injective modules.In the third chapter,we study n-strongly Gorenstein graded modules,some properties of n-strongly Gorenstein gr-projective,gr-injective and gr-flat modules are characterized.An example is given to show that n-strongly Gorenstein gr-injective modules need not be m-strongly Gorenstein gr-injective modules whenever positive integers n>m.Also,many properties of n-strongly Gorenstein gr-injective modules and n-strongly Gorenstein gr-flat modules are given,and some known results are generalized.