A GENERALIZATION OF CORETRACTABLE MODULES

Let R be a ring and M a right R-module. We call M , coretractable relative to Z(M ) (for short, Z(M )-coretractable) provided that, for every proper submodule N of M containing M Z(M ), there exists a nonzero homomorphism f : N → M . We investigate some conditions under which two concepts of coretractable and Z(M )-coretractable, coincide. For a commutative semiperfect ring R, we show that R is Z(R)-coretractable if and only if R is a Kasch ring. Some examples are provided to illustrate different concepts.