| 关于强正则环的几个等价刻划 |
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| 引用本文： | 方茵,雷震.关于强正则环的几个等价刻划[J].洛阳师范学院学报,2004,23(2):20-21. |
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| 作者姓名： | 方茵 雷震 |
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| 作者单位： | 1. 芜湖市职教中心,安徽芜湖,241000
2. 芜湖师范专科学校数学系,安徽芜湖,241008 |
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| 摘 要： | 设R是一个环 ,如果对于任意的x ,y∈R ,有xy -yx∈C(R) ,那么下列条件等价 :( 1 )R是强正则环 ;( 2 )R是VonNeumann正则环 ;( 3)R是广义正则环 .设R是半可换环 ,则以下条件等价 :( 1 )R是强正则环 ;( 2 )R的每一个极大的本质的左理想是左GP -内射模 ;( 3)R的每一个极大的本质的右理想是右GP -内射模 .
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| 关 键 词： | 强正则环 正则环 广义正则环 半可换环 GP-内射模 |
| 文章编号： | 1009-4970(2004)02-0020-02 |
| 修稿时间： | 2003年12月26 |
Some Characterizations on Strongly Regular Rings |
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| FANG Yin ,LEI Zhen.Some Characterizations on Strongly Regular Rings[J].Journal of Luoyang Teachers College,2004,23(2):20-21. |
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| Authors: | FANG Yin LEI Zhen |
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| Institution: | FANG Yin 1,LEI Zhen 2 |
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| Abstract: | Let R is a ring,if xy-yx∈C(R),for all x,y∈R,then following statements are equivalent: (1)R is a strongly regular ring,(2)R is a Von Neumann regular ring,(3)R is a generalized regular ring;Let R is a semi commutative ring,then following statements are equivalent:(1)R is a strongly regular ring,(2)Every maximal essential left ideals of R are left GP-injective modules,(3)Every maximal essential right ideals of R are right GP-injective modules. |
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| Keywords: | strongly regular rings Von Neumann regular rings generalized regular rings semi commutative rings GP-injective modules |
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