N-coretractable modules

Let ? be a ring and ? a right ?-module. Let ? be a proper submodule of ?. We call ?, coretractable relative to ?, (for short N-coretractable) provided that, for every proper submodule ? of ? containing ?, there is a nonzero homomorphism ? ∶ ?/? → ?. We present some conditions that a module ? is coretractable if and only if ? is coretractable relative to a submodule ?. We also provide some examples to illustrate special cases.

Keywords:

coretractable modules , N-coretractable modules