Abstract: 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.

Key words: Closed submodules, Closed weak supplemented, Small submodule

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