When some complement of an exact fully invariant submodule is a direct summand

Abstract

In this paper, we study modules with the property that every exact fully invariant submodule has a complement which is a direct summand. This new class of modules properly contains both of classes of FI-extending modules and C11r-modules (i.e. modules have C11 property for exact submodules). We obtain several module theoretical results including decompositions for the former class of modules.