Let R be a ring. An R-module M is called semi-co-Hopfian if any injective endomorphism of M has a direct summand image. Let R be a commutative ring with    be the class of finitely generatedR-modules;  be the class of co-Hopfian R-modules and  be the class of semi-co-Hopfian R-modules.

We have  and in [8] Vasconcelos proved that if R is a commutative ring whose all prime ideals are maximal, then  hence

In this article, we characterize commutative rings R on which a module M is semi-co-Hopfian if and only if M is finitely generated, i.e.,

semi-FGI-ring, principal ideal ring, finitely generated module, finitely annihilated module, semi-co-Hopfian module, co-Hopfian module.