General Injective Modules And General PP-rings

In this thesis, we mainly investigate several general injective modules, general pp rings, and the relationships between them. The general injective modules referred to are weak Cs module, Cess module and Ecs module, general pp rings contains Gpp ring, pp — ideal and pp ring.The thesis mainly revolves several kinds of general injective modules and pp rings introduced above to launch the discussion, thus we buildthe bridge between injectivity and projectivity. The obtained results have certain significance to the research of Ring- Theory and Module-Theory.The thesis is divided into four chapters.The first chapter is introduction , we outline some important work about the thesis.In chapter 2 , we first give the conception of "Ecs module" .which is a general injective module, then we investigate some direct — sum properties of Ecs module and some other general injective modules such as weak Cs module, Cess module, obtain the conclusion below : Let M =(?)_i∈I M_i, then (1) suppose M_i is (nearly) M_j-injective(i≠j∈I), Mis weak Cs module if and only if M_i is weak Cs module((?)i∈I). (2) M is Ecs module if and only if M_i is Ecs module ((?)i∈I).In chapter 3, we introduce the conception of " pp — ideal" ,...