- Turkish Journal of Mathematics
- Vol: 31 Issue: 4
- An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules
An Example of an Indecomposable Module Without Non-Zero Hollow Factor Modules
Authors : Christian Lomp
Pages : 415-419
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :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 [2].Keywords : Hollow modules, Indecomposable modules, Lifting modules, coalgebras