On M-C-injective and self-c-injective modules

Abstract

Let M 1 and M 2 be two R-modules. Then M 2 is called M 1-c-injective if every homomorphism α from K to M 2, where K is a closed submodule of M 1, can be extended to a homomorphism β from M 1 to M 2. An R-module M is called self-c-injective if M is M-c-injective. For a projective module M, it has been proved that the factor module of an M-c-injective module is M-c-injective if and only if every closed submodule of M is projective. A characterization of self-c-injective modules in terms endomorphism ring of an R-module satisfying the CM-property is given. © 2010 World Scientific Publishing Company.