İnvestigation of i̇njektivity of nonsingular modules

Let R be an associative ring with identity. Given right R-modules A and B, A is said to be B-subinjective if for every monomorphism ı : B → C and for every homomorphism f : B → A, there exists a homomorphism h : C → A such that hı=f. The subinjectivity domain of a module A is defined to be the class of modules B such that A is B-subinjective. In this thesis, through the notions proper class and subinjectivity, injectivity of nonsingular modules is studied, which are the generalization of torsionless (or torsion-free) abel groups. The smallest possible subinjectivity domain of a nonsingular module is determined, and nonsingular modules which have this domain are investigated. Keywods: Injective modules, subinjectivity domains, nonsingular modules, proper classes.