| 分次环的分次Excellent扩张 |
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| 引用本文： | 任艳丽,王尧. 分次环的分次Excellent扩张[J]. 数学研究及应用, 2007, 27(3): 586-590 |
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| 作者姓名： | 任艳丽 王尧 |
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| 作者单位： | 南京晓庄学院数学系,江苏,南京,210017 |
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| 基金项目： | 国家自然科学基金;辽宁省教育厅资助项目 |
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| 摘 要： | 本文引进了分次环的分次Excellent扩张概念,设S=⊕_(g∈G)S_g是R=⊕_(g∈G)R_g的分次Excellent扩张,证明了S是分次右V-环当且仅当R是分次右V-环,S是分次PS-环当且仅当R是分次PS-环,S是分次Von Neumann正则环当且仅当R是分次Von Neumann正则环。
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| 关 键 词： | 分次Excellent扩张 分次右V-环 分次PS-环 分次Von Neumann正则环. |
| 文章编号： | 1000-341X（2007）03-0586-05 |
| 收稿时间： | 2005-06-07 |
| 修稿时间： | 2006-07-02 |
Graded Excellent Extensions of Graded Rings |
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| REN Yan-li and WANG Yao. Graded Excellent Extensions of Graded Rings[J]. Journal of Mathematical Research with Applications, 2007, 27(3): 586-590 |
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| Authors: | REN Yan-li and WANG Yao |
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| Affiliation: | Department of Mathematics, Nanjing Xiaozhuang University, Jiangsu 210071, China;Department of Mathematics, Nanjing Xiaozhuang University, Jiangsu 210071, China |
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| Abstract: | The concept of graded excellent extension of graded rings is introduced. Let $S=bigoplus_{gin G}S_g$ be a graded excellent extension of $R=bigoplus_{gin G}R_g$. We prove that $S$ is a graded right $V$-ring if and only if $R$ is a graded right $V$-ring, $S$ is graded $PS$-ring if and only if $R$ is a graded $PS$-ring, and $S$ is a Von Neumann regular ring if and only if $R$ is a graded Von Neumann regular ring. |
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| Keywords: | graded excellent extension graded right V-ring graded PS-ring graded Von Neumann regular ring. |
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