On closed weak supplemented modules

A module M is called closed weak supplemented if for any closed submodule N of M, there is a submodule K of M such that M = K + N and K∩N≪M. Any direct summand of closed weak supplemented module is also closed weak supplemented. Any nonsingular image of closed weak supplemented module is closed weak supplemented. Nonsingular V-rings in which all nonsingular modules are closed weak supplemented are characterized in Section 4.