Abstract
We introduce the notion of FI-retractable modules which is a generalization of retractable modules. A module is called FI-retractable if for every nonzero fully invariant submodule N of M, Hom(M,N) is not 0. Wee continue the study of FI-retractable modules. Amongst other structural properties, we also deal direct sums and direct summands of FI-retractable modules. The last section of the paper is devoted to study of End(M), such that M is FI-retractable.
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