On closed weak supplemented modules  

作　　者：曾庆怡 史美华 

机构地区：[1]Department of Mathematics, Zhejiang University [2]Department of Mathematic, Shaoguan University, Shaoguan 512005, China [3]Department of Mathematics, Zhejiang Education Institute, Hangzhou 310012, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2006年第2期210-215,共6页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project (No. 102028) supported by the Natural Science Foundation of Zhejiang Province, China

摘　　要：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.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.

关 键 词：Closed submodules Closed weak supplemented Small submodule 

分 类 号：O153.3[理学—数学]