| 关于强正则环的一些研究 |
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| 引用本文： | 崔顺,吴俊.关于强正则环的一些研究[J].安徽师范大学学报(自然科学版),2010,33(2):108-110. |
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| 作者姓名： | 崔顺 吴俊 |
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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： | 安徽省教育厅自然科学研究重点项目 |
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| 摘 要： | 主要证明了下列条件等价:(1)R是强正则环;(2)R是ELT-的半素环,且对于R的每一个本质左理想L,(R/L)R是平坦模,R的每一个极大左理想或极大右理想是GW-理想;(3)R是ZC-环,R的每一个极大本质左理想是GW-理想且R的每一个单奇异左模是GP-同射模或平坦模.
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| 关 键 词： | SF-环 ZC-环 GW-理想 von Neumann正则环 强正则环 |
Some Studies on Strongly Regular Rings |
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| CUI Shun,WU Jun.Some Studies on Strongly Regular Rings[J].Journal of Anhui Normal University(Natural Science Edition),2010,33(2):108-110. |
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| Authors: | CUI Shun WU Jun |
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| Institution: | CUI Shun,WU Jun(College of Mathematics and Computer Science,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | In this paper,we mainly proved that the following conditions are equivalent:(1) R is a strongly regular ring;(2) R is a ELT-semi-prime ring,and for every essential left ideal L of R,(R/L)R is flat,every maximal left ideal or maximal right ideal of R is GW-ideal;(3) R is a ZC-ring,every maximal essential left ideal of R is GW-ideal and every simple singular left R-module is either GP-injective or flat. |
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| Keywords: | SF-ring ZC-ring GW-ideal von Neumann regular ring strongly regular ring |
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