On quasi-regular torsion-free modules

摘要

A torsion-free module is called quasi-regular if each cyclic submodule is a quasi-summand. This article characterizes torsion-free Abelian groups that are quasi-regular as modules over a subring of their endomorphism ring. In particular, if G is a torsion-free Abelian group such that its ring Q E of quasi-endomorphisms is Artinian, then the left E -module G is quasi-regular if and only if the left C -module G is quasi-regular, where C is the center of its endomorphism ring E .