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 Z(M), there exists a nonzero homomorphism f :M/N→ M. We investigate some conditions under which two concepts of core- tractable 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.
