| 单位正则环和SF-环 |
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| 引用本文： | 葛平红,储茂权.单位正则环和SF-环[J].安徽师范大学学报(自然科学版),2009,32(4):322-324. |
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| 作者姓名： | 葛平红 储茂权 |
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| 作者单位： | 安徽师范大学数学计算机科学学院,安徽,芜湖,241000;安徽师范大学数学计算机科学学院,安徽,芜湖,241000 |
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| 基金项目： | Supported by Natural Science Foundation of Education Department of Anhui Province(KJ2008A026); Natural Science Foundation of Colleges and Universities of Anhui Province(KJ2009B107Z). |
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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,单位正则环是SF-环,但SF-环是否为单位正则却未有结果.本文主要研究左SF-环成为单位正则环的条件及在一定条件下SF-环与单位正则环的等价性.
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| 关 键 词： | SF-环 单位正则环 强正则环 正则环 |
Unit Regular Rings and SF-rings |
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| GE Ping-hong,CHU Mao-quan.Unit Regular Rings and SF-rings[J].Journal of Anhui Normal University(Natural Science Edition),2009,32(4):322-324. |
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| Authors: | GE Ping-hong CHU Mao-quan |
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| Institution: | GE Ping-hong,CHU Mao-quan(College of Mathematics , Computer Science,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | A ring R is defined to be a left SF-ring if all simple left R-modules are flat.It is well known that unit regular rings are SF-rings.But the question whether a left SF-ring is necessarily unit regular remains unanswered.In this paper,we mainly study some conditions that left SF-rings turn into unit regular rings and the equivalence that left SF-rings and unit regular rings are encircled under certain conditions. |
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| Keywords: | SF-ring unit regular ring strongly regular ring regular ring |
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