| 摘要: |
| 本文研究类似于VNL环的环的性质.称一个环R是几乎弱正则环（几乎π-正则环，几乎强π-正则环），如果对任意的a ∈ R，都有a或1-a是弱正则（π-正则，强π-正则）元.本文讨论这些新环的扩张，给出相关环之间的关系图，拓广了局部环和VNL环的研究. |
| 关键词: 几乎弱正则环 几乎π-正则环 几乎强π-正则环 环扩张 |
| DOI： |
| 分类号:O153.3 |
| 基金项目:国家自然科学基金资助项目（11101217）；江苏省自然科学基金资助项目（BK20141476）. |
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| SOME RINGS SIMILAR TO THE VNL RINGS |
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WANG Yao1, YANG Zhen1, REN Yan-li2
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1.School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;2.School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, China
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| Abstract: |
| In this paper, we investigate the properties of rings similar to the VNL rings. A ring R is said to be a almost weakly regular ring (almost π-regular ring, almost strongly π-regular ring), provided that for any a ∈ R, either a or 1-a is weakly regular (π-regular, strongly π-regular). We discuss extensions of these new rings and give the relationship between relevant rings, which extend the study of local rings and VNL rings. |
| Key words: almost weakly regular ring almost π-regular ring almost strongly π-regular ring ring extension |
