Radically Prime Decompositions Of Ideals And GPF Modules

In this thesis , we mainly investigate radically prime decompositions of ideals , GPF modules and GPF rings. We divide the thesis in four chapters. The first chapter is introduction,in this chapter, we have attempted to outline the subjects connecting with our work.In chapter 2 , we have enlarged the general theory on the Pre-Decompositions of ideals. First, we have defined the radically prime ideal based on the pre-prime ideal and then the radically prime decompositions of ideals are studied .At last , we have discussed some interesting results of the primary decompositions of radically ideals.In chapter 3 , GPF modules are studied. First, we show some relations between GPF modules and GP injective modules. Second, some properties about GPF modules are discussed .At last, we give a characterization of GP coherent rings.In chapter 4 , GPF rings are considered , in the chapter , we mainly study some properties about GPF rings satisfying some additional conditions . Finally the connections of GPF rings and GPF modules is given.