Some characterizations on hollow-lifting modules

Abstract

Let R be any ring and let M be any right R-module. M is called hollow-lifting if every submodule N of M such that  is hollow has a coessential submodule that is a direct summand of M. In these notes, we show that an R-module M is hollow-lifting if and only if for every submodule N of M with  hollow has a strong supplement in M. We establish a condition under which a direct sum of hollow modules is hollow-lifting.

Keywords:   Lifting modules, Hollow-lifting modules