A module Mis called closed weak d-supplemented if for any closed submodule Nof M, there is a submodule Kof Msuch that  and  Any direct summand of closed weak d-supplemented module is also closed weak d-supplemented. Any nonsingular image of closed weak d-supplemented module is closed weak d-supplemented. Nonsingular V-rings in which all nonsingular modules are closed weak d-supplemented are also characterized in Section 4.

closedsubmodules,closedweakd-supplemented,d-small submodule.