Almost-Injective Modules and Almost-Projective Modules

Abstract

In this thesis, some almost injective modules and almost projective modules are investigated. We give some new properties of almost injective modules and their endomorphism rings and also provide conditions as to when a direct sum of almost injective (or CS) modules is again almost injective (or CS) in some special cases. We also describe rings over which every right module is almost injective. Moreover, we give a description of rings over which every simple module is almost projective. In addition, the characterization of the module M such that every simple module is almost projective (respectively, almost injective) in the category δ(M) is discussed.