A module M is called hollow-lifting if every submodule N of M such that M/N is hollow contains a direct summand D \subseteq N such that N/D is a small submodule of M/D. A module M is called lifting if such a direct summand D exists for every submodule N. We construct an indecomposable module M without non-zero hollow factor modules, showing that there are hollow-lifting modules which are not lifting. The existences of such modules had been left open in a recent work by N. Orhan, D. Keskin-Tütüncü and R. Tribak .
LOMP, CHRISTIAN (2007) "An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules," Turkish Journal of Mathematics: Vol. 31: No. 4, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol31/iss4/8