A Study On Projective Modules and Some Weak forms of Projectivity

In this thesis we consider projective modules and some weak forms of projectivity and we try to study the most important known results concerning these modules. In chapter one we summarize some of the essential and basic concepts in and n. This chapter consists of three sections; section l presents definitions and basic properties of modules. In section 2, we study the radical of modules and rings which plays an important role in our study. In section 3 we study simple and semi simple modules and rings. In chapter Two, which is the main body of our thesis, we study the main characterizations and properties of projective modules. Moreover we study radicals and endomorphism rings of projective modules. Finally, "projective covers" was studied in this chapter. In chapter three we study semi-perfect and perfect rings as an a applications to projective modules, those over which all finitely generated modules and, respectively, all modules have projective covers. 5 2 9 51 9 In chapter four, we study some weak forms of projective modules such as, weakly projective modules, ideal projectivity , Jacobson radical projectivity, and simple projectivity.