On small principally injective rings

Abstract

The purposes of this thesis are (1) to study properties and characterizations of small principally injective modules, (2) to study properties and characterizations of small principally injective rings, and (3) to find some relations between small principally injective modules, small principally injective rings and projective modules.

Let R be a ring. A right R-module M is called principally injective if every R-homomorphism from a principal right ideal of R to M can be extended to an R-homomorphism from R to M. A right R-module M is called small principally injective if every R-homomorphism from a small and principal right ideal of R to M can be extended to an R-homomorphism from R to M...