Let 𝑅 be a ring and 𝑀 a right 𝑅-module. Let 𝑁 be a proper submodule of 𝑀. We call 𝑀, coretractable relative to 𝑁, (for short N-coretractable) provided that, for every proper submodule 𝐾 of 𝑀 containing 𝑁, there is a nonzero homomorphism 𝑓 ∶ 𝑀/𝐾 → 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.
