
Vietnam Journal of Mathematics 34:1(2006)
1730

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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