Let R be a ring and M a right R-module. Let N be a proper submodule of M. We say that M is N-coretractable (or M is coretractable relative to N) provided that, for every proper submodule K of M containing N, there is a nonzero homomorphism f : M=K\rightarrow M. We present some conditions that a module M is coretractable if and only if M is coretractable relative to a submodule N. We also provide some examples to illustrate special cases.
