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 $M/N$ 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 hollowlifting modules is hollow-lifting.