| N-环Von-Neumann正则性 |
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| 引用本文： | 吴俊,殷晓斌.N-环Von-Neumann正则性[J].数学研究及应用,2001,21(2):267-272. |
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| 作者姓名： | 吴俊 殷晓斌 |
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| 作者单位： | 南京大学数学系,;安徽师范大学数学系, |
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| 摘 要： | 环R称为N-环，如果R的素根N(R)=｛r∈R｜存在自然数n使rn=0}.本文不仅对N-环进行了刻划，而且还研究了N-环的VonNeumann正则性.特别证明了：对于N-环R，如下条件是等价的：(1)R是强正则环；(2)R是正则环；(3)R是左SP-环；(4)R是右SF-环；(5)R是MELT，左p-V-环；(6)R是MERT，右p-V-环.因此推广了文献4]中几乎所有的重要结果，同时也改进或推广了其它某些有关正则环的有用结果.
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| 关 键 词： | 正则环 N-环 SF-环 p-V-环. |
| 文章编号： | 1000-341X(2001)02-0267-06 |
| 收稿时间： | 1/5/1998 12:00:00 AM |
| 修稿时间： | 1998年1月5日 |
Von-Neumann Regularity of N-rings |
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| WU Jun and YIN Xiao-bin.Von-Neumann Regularity of N-rings[J].Journal of Mathematical Research with Applications,2001,21(2):267-272. |
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| Authors: | WU Jun and YIN Xiao-bin |
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| Institution: | Dept. of Math., Nanjing University, Jiangsu 210093, China;Dept. of Math., Anhui Normal Uuiversity, Wuhu, 241000, China;Dept. of Math., Nanjing University, Jiangsu 210093, China;Dept. of Math., Anhui Normal Uuiversity, Wuhu, 241000, China |
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| Abstract: | A ring R is called a N-ring if N(R) ={r R | there is a natural number n such that rn = 0}. In this paper, some new characterization of N-rings are given. Furthermore, the Von Neumann regularity of N-rings is also considered. Particularly, we show the following result: for a N-ring R, the following conditions are equivalent: (1) R is a strongly regular ring; (2) R is a regular ring; (3) R is a left SF-ging; (4) R is right SF-ring; (5) R is a MELT, left p-V-ring; (6) R is a MERT, right p-V-ring. |
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| Keywords: | regular rings N-rings SF-rings SF-rings p-V-rings |
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