| 关于单位正则环 |
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| 引用本文： | 陈焕银.关于单位正则环[J].数学进展,2007,36(4):435-440. |
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| 作者姓名： | 陈焕银 |
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| 作者单位： | 湖南师范大学数学与计算机科学学院,长沙,湖南,410006 |
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| 摘 要： | 本文得到了单位正则环的一个新特征,证明了:正则环R为单位正则环当且仅当存在理想I使得(1)R/I为单位正则环;(2)对任何a∈R,存在理想J满足JI=0和a=aua,其中u模J左可逆.作为应用,利用零化子理想刻画了单位正则环.
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| 关 键 词： | 单位正则 伪相似 零化子 |
| 文章编号： | 1000-0917（2007）04-0435-06 |
| 修稿时间： | 2005-06-06 |
On Unit Regular Rings |
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| CHEN Huanyin.On Unit Regular Rings[J].Advances in Mathematics,2007,36(4):435-440. |
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| Authors: | CHEN Huanyin |
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| Institution: | Department of Mathematics, Hunan Normal University, Changsha, Hunan, 410006, P. R. China |
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| Abstract: | In this paper, we get a new characterization of unit-regular rings. A regular ring R is unit-regular if and only if there exists an ideal I such that (1) R/I is unit-regular. (2) For each a ∈ R there exist an ideal J such that JI = 0 and a = aua, where u ∈ R is left invertible modulo J. As an application we prove that a regular ring R is unit-regular if and only if there exists an ideal I of R such that R/I and R/r.ann(I) are unit-regular. |
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| Keywords: | unit regular ring pseudo-similarity annihilator |
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