On generalized extending modules

A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.