Some Results on C-retractable Modules (European Journal of Pure and Applied Mathematics, 2020)
An R-module M is called c-retractable if there exists a nonzero homomorphism from M to any of its nonzero complement submodules. In this paper, we provide some new results of c- retractable modules. It is shown that every projective module over a right SI-ring is c-retractable. A dual Baer c-retractable module is a direct sum of a Z2-torsion module and a module which is a direct sum of nonsingular uniform quasi-Baer modules whose endomorphism rings are semi- local quasi-Baer. Conditions are found under which, a c-retractable module is extending, quasi-continuous, quasi-injective and retractable. Also, it is shown that a locally noetherian c-retractable module is homo-related to a direct sum of uniform modules. Finally, rings over which every c-retractable is a C4-module are determined.