| von-Neumann正则环与左SF-环 |
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| 引用本文： | 周海燕,王小冬. von-Neumann正则环与左SF-环[J]. 数学研究及应用, 2004, 24(4): 679-683 |
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| 作者姓名： | 周海燕 王小冬 |
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| 作者单位： | 1. 南京大学数学系,江苏,南京,210093
2. 安徽工程科技学院应用数理系,安徽,芜湖,241000 |
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| 基金项目： | 安徽省教育厅自然科学基金(2003kj166),安徽省高校青年教师基金(2003jq107)资助项目. |
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| 摘 要： | 环R称为左SF-环,如果每个单左R-模是平坦的.众所周知,Von-Neumann正则环是SF-环,但SF-环是否是正则环至今仍是公开问题,本文主要研究左SF-环是正则环的条件,证明了:如果R是左SF-环且R的每个极大左(右)理想是广义弱理想,那么R是强正则环.并且推广了Rege[3]中的相应结果.
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| 关 键 词： | 正则环 强正则环 SF-环 广义弱理想 |
| 文章编号： | 1000-341X(2004)04-0679-05 |
| 收稿时间： | 2002-04-23 |
| 修稿时间： | 2002-04-23 |
On von-Neumann Regular Rings and Left SF-Rings |
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| ZHOU Hai-yan and WANG Xiao-dong. On von-Neumann Regular Rings and Left SF-Rings[J]. Journal of Mathematical Research with Applications, 2004, 24(4): 679-683 |
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| Authors: | ZHOU Hai-yan and WANG Xiao-dong |
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| Affiliation: | Dept. of Math.; Nanjing University; Jiangsu; China;Dept. of Appl. Math. & Phys.; Anhui University of Science and Technology; Wuhu; China |
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| Abstract: | A rings R is defined to be a left SF-ring if all simple left R -modules are flat. It is known that von Neumann regular rings are SF-rings. But the question whether a left SF-ring is necessarily regular remains open. In this paper, we study the regularity of left SF-rings which satisfy certain additional conditions. It is proved that R is strongly regular if R is a left SF-ring whose maximal left (right) ideals are generalized weak ideals. Furthermore, we generalize some results in [3]. |
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| Keywords: | regular ring strongly regular ring SF-ring generalized weak ideal. |
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