| 拟polar环的注记（英文） |
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| 引用本文： | 崔建,陈建龙.拟polar环的注记（英文）[J].数学研究,2012,45(2):167-174. |
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| 作者姓名： | 崔建 陈建龙 |
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| 作者单位： | 1. 东南大学数学系,江苏南京210096／安徽师范大学数学系,安徽芜湖241000
2. 东南大学数学系,江苏南京,210096 |
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| 基金项目： | supported by Foundation item:the NSF of China(10971024);the Specialized Research Fund for the Doctoral Program of Higher Education(200802860024) |
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| 摘 要： | 称一个环R中的元素a是拟polar元,若存在p2=P∈R满足p∈comm_R~2（a）,a＋P∈U（R）并且ap∈R~（qnil）;且称环R是拟polar的如果R中每一个元素都是拟polar元.本文证明了,任一环R中强π-正则元是拟polar的,而拟polar元是强clean的.拟polar环的一些扩张性质也作了探讨.
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| 关 键 词： | 拟polar环 强clean环 强π-正则环 谱幂等元 |
Notes on Quasipolar Rings |
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| Cui Jian,Chen Jianlong.Notes on Quasipolar Rings[J].Journal of Mathematical Study,2012,45(2):167-174. |
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| Authors: | Cui Jian Chen Jianlong |
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| Institution: | 1 (1.Department of Mathematics,Southeast University,Nanjing Jiangsu 210096; 2.Department of Mathematics,Anhui Normal University.Wuhu Anhui 241000) |
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| Abstract: | Abstract An element a in a ring R is called quasipolar if there exists p2= p∈R such that p∈commR2（a）,a + p∈U（R） and ap∈Rqnil;and a ring R is said to be quasipolax in case every element of R is quasipolax.In this note,we prove that any strongly 7r-regular element in a ring R is quasipolar,and any quasipolar element in R is strongly clean.Several extension properties of quasipolar rings are also investigated. |
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| Keywords: | Quasipolar ring Strongly clean ring Strongly π-regular ring Spectral idempotent |
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