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Vietnam Journal of Mathematics 34:1(2006) 17-30

Closed Weak Supplemented Modules 

Qingyi Zeng

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 a closed weak supplemented module is also closed weak supplemented. Any finite direct sum of local distributive closed weak supplemented modules is also closed weak supplemented. Any nonsingular homomorphic image of a closed weak supplemented module is closed weak supplemented. R is a closed weak supplemented ring if and only if M_n(R) is also a closed weak supplemented ring for any positive integer n.

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