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Received: 2004-11-22

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.2 P.210~215

http://doi.org/10.1631/jzus.2006.A0210


On closed weak supplemented modules


Author(s):  Zeng Qing-yi, Shi Mei-hua

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   zqy67@163.com

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


Zeng Qing-yi, Shi Mei-hua. On closed weak supplemented modules[J]. Journal of Zhejiang University Science A, 2006, 7(2): 210~215.

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author="Zeng Qing-yi, Shi Mei-hua",
journal="Journal of Zhejiang University Science A",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A0210"
}

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T1 - On closed weak supplemented modules
A1 - Zeng Qing-yi
A1 - Shi Mei-hua
J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2006.A0210


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 KN<<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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Alizade, R., Büyükasik, E., 2003. Cofinitely weak supplemented modules. Comm. Alg., 31(11):5377-5390.

[2] Chatters, A.W., Khuri, S.M., 1980. Endomorphism rings of modules over nonsingular CS rings. J. London Math. Soc.(2), 21:434-444.

[3] Goodearl, K.R., 1976. Ring Theory. New York and Basel.

[4] Harmanci, A., Keskin, D., Smith, P.F., 1999. On ⊕-supplemented modules. Acta Math. Hungar., 83(1/2):161-169.

[5] Wisbauer, R., 1991. Foundations of Modules and Rings Theory. Gordon and Brench.

[6] Wisbauer, R., 1996. Modules and Algebras: Bi-module Structure and Group Actions on Algebras. Pitman Monographs and Surveys in Pure and Applied Mathematics 81.

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