Let R be a ring and M a right R-module. We call M, a δ(M)-coretractable module if for every proper submodule N of M containing δ(M), there is a nonzero homomorphism from M/N to M. We investigate some conditions which under two concepts δ(M)-coretractable and coretractable coincide. For a ring R, we prove that R is right Kasch if and only if RR is δ(RR)-coretractable.
