| 关于单奇异YJ-内射模与正则环的刻画 |
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| 引用本文： | 丁力.关于单奇异YJ-内射模与正则环的刻画[J].安庆师范学院学报(自然科学版),2009,15(1):1-3. |
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| 作者姓名： | 丁力 |
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| 作者单位： | 安徽师范大学,数学与计算机科学学院,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： | 通过拟理想对环的正则性进行刻画，证明了：（1）环R是强正则环当且仅当R是Abelian的左GP—y’－环，且R的每个极大本质左理想是拟理想；（2）若环R的每个极大本质左理想是拟理想，则R是正则环当且仅当R是左AGP－内射的左GP—V’－环。
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| 关 键 词： | 强正则环 von Neumann正则环 YJ-内射模 GP-V’-环 拟理想 |
On Simple Singular YJ-injective Modules and Characterizations of Regular Rings |
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| DING Li.On Simple Singular YJ-injective Modules and Characterizations of Regular Rings[J].Journal of Anqing Teachers College(Natural Science Edition),2009,15(1):1-3. |
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| Authors: | DING Li |
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| Institution: | DING Li (School of Math. and Computer Science, Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | In this paper,two results on the regularity of rings characterized by their quasi-ideal are mainly obtained:(1)R is a strongly regular ring if and only if R is Abelian left GP-V′-ring whose every maximal essential left ideal is a quasi-ideal.(2)If R is a ring whose every maximal essential left ideal is a quasi-ideal,then R is regular if and only if R is a left AGP-injective left GP-V′-ring. |
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| Keywords: | strongly regular ring von Neumann regular ring YJ-injective GP-V′-ring quasi-ideal |
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