Some Generalizations of Quasi-Projective Modules

Abstract

Our main goal in this dissertation is to investigate semi-projective modules, direct projective modules and SGQ-projective modules, which are generalizations of quasi-projective modules and to discover new properties and new characterizations of these modules.In the first chapter,we give preliminary notions and some results.The second chapter is devoted to semi-projective modules.We study some basic properties of such modules and provide some new characterizations.In the third chapter, we define SGQ-projective modules.Some properties of this modules and its endomorphism rings are studied.In the fourth chapter, we first investigate some connections between the notions of epi projectivity, epi K-projectivity, epi K*-projectivity.Chapter 5, is concerned with modules over formal triangular matrix rings.In this last chapter, our results focus on relative projectivity and lifting properties of modules.