General Injectivity And Flatness

In this thesis,we mainly investigate genaral injectivity and one special ring about injectivity and flatness .The first chapter is introduction.in this chapter,we have briefly attempted to outline the important position of injectivity and flatness in algebras,and the developments in mathematics,with particular attention to the subjects connecting with our work.The second chapter mainly studies SIS rings,in the chapter,we consider some properties about SIS rings,get some relations of SIS rings and other special rings,finally some characterization of categories on SIS rings are also given.The main result as followings:For every left R-module M,SocM = M,then R is SIS ring;R is SIS ring if and only if R is a self-injective regular ring if and only if R is a self-injective ring such that the left annihilator of each element of R is a cyclic flat left R-module if and only if R is a self-injective ring such that every principal right ideal is a maximum right annihilator or a right nonsingular right SF ring of projective right annihilator of some element of R.In chapter 3,some properties of Quasi-injective modules , Quasi-injective pre-covers and Quasi-injective covers are considered.Meantime,we also study some equivalence relations of Quasi-injective,Quasi-injective cover is unique to within isomorphism and the transitivity of Quasi-injective precover.The main result as followings:...