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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2006, Vol. 7 Issue (2 ): 16-    DOI: 10.1631/jzus.2006.A0210
    
On closed weak supplemented modules
Zeng Qing-yi, Shi Mei-hua
Department of Mathematics, Zhejiang University, Hangzhou 310027, China; Department of Mathematic, Shaoguan University, Shaoguan 512005, China; Department of Mathematics, Zhejiang Education Institute, Hangzhou 310012, China
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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     
Received: 22 November 2004     
CLC:  O153.3  
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Zeng Qing-yi, Shi Mei-hua. On closed weak supplemented modules. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(2 ): 16-.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2006.A0210     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2006/V7/I2 /16

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