On coretractable modules
A right \(R\)-module \(M\) is called: (i) coretractable if \(\text{Hom}_R(M/K,M)\neq 0\) for every proper submodule \(K\) of \(M\); (ii) mono-coretractable if there is a monomorphism from \(M/K\) to \(M\) for every submodule \(K\) of \(M\). The authors prove that every right \(R\)-module is coretractable if and only if \(R\) is right perfect, and every right \(R\)-module is small coretractable if and only if all torsion theories on \(R\) are cohereditary. They also show that coretractable modules are a proper generalization of mono-coretractable modules.
scientific article; zbMATH DE number 6537499