A NOTE ON SELF-SMALL MODULES OVER RM-DOMAINS

Abstract

This paper provides two new characterizations of RM-domains, i.e. domains satisfying the restricted minimum condition. A Noetherian domain is a RM-domain if and only if every torsion module is a direct sum of submodules whose cyclic submodules have finite length and homogeneous composition series. We show that this occurs exactly if all self-small torsion modules are finitely generated.