Modules and abelian groups with minimal (pure-) projectivity domains

Abstract

In this paper, we give a complete description of the projectively poor abelian groups and prove that there exists a pure projectively poor abelian group. We show that over a commutative Artinian ring every module having a projectively poor factor module by a pure submodule, is itself projectively poor. We also give some other properties of pure projectively poor modules.