BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, cilt.43, sa.7, ss.2227-2231, 2017 (SCI-Expanded)
A module M is called FI-extending if every fully invariant submodule of M is essential in a direct summand of M. It is not known whether a direct summand of an FI-extending module is also FI-extending. In this study, it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?