On hollow-lifting modules

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 M/N is hollow has a coessential submodule that is a direct summand of M. We prove that every amply supplemented hollow-lifting module with finite hollow dimension is lifting. It is also shown that a direct sum of two relatively projective hollow-lifting modules is hollow-lifting.