| $GP$-$V^{'}$-环的非奇异性与正则性 |
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| 引用本文： | 殷晓斌,王瑞,李小龙.$GP$-$V^{'}$-环的非奇异性与正则性[J].数学研究及应用,2011,31(6):1003-1008. |
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| 作者姓名： | 殷晓斌 王瑞 李小龙 |
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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;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： | 国家自然科学基金(Grant Nos.10871106;10901002;10971099),安徽省教育厅自然科学基金(Grant No.KJ2008A026). |
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| 摘 要： | In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such that an = 0 and anRbn = 0.The non-singularity and regularity of quasi ZI,GP-Vˊ-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results.
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| 关 键 词： | 非奇异性 戒指 非零元素 强正则环 正整数 子环 |
| 收稿时间： | 2010/8/31 0:00:00 |
| 修稿时间： | 2010/11/26 0:00:00 |
The Non-Singularity and Regularity of $GP$-$V'$-Rings |
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| Xiao Bin YIN,Rui WANG and Xiao Long LI.The Non-Singularity and Regularity of $GP$-$V'$-Rings[J].Journal of Mathematical Research with Applications,2011,31(6):1003-1008. |
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| Authors: | Xiao Bin YIN Rui WANG and Xiao Long LI |
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| Institution: | College of Mathematics and Computer Science, Anhui Normal University, Anhui 241000, P. R. China |
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| Abstract: | In this paper, we introduce a non-trivial generalization of $ZI$-rings-quasi $ZI$-rings. A ring $R$ is called a quasi $ZI$-ring, if for any non-zero elements $a,b\in R$, $ab=0$ implies that there exists a positive integer $n$ such that $a^{n}\neq 0$ and $a^{n}Rb^{n}=0$. The non-singularity and regularity of quasi $ZI$, $GP$-$V'$-rings are studied. Some new characterizations of strong regular rings are obtained. These effectively extend some known results. |
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| Keywords: | $GP$-$V'$-rings quasi $ZI$-rings MELT(MERT) rings weakly regular rings generalized regular rings |
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