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 [Formula: see text]-modules (i.e. modules have [Formula: see text] property for exact submodules). We obtain several module theoretical results including decompositions for the former class of modules.
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Tercan et al. (2024) studied this question.
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