| Exchange Rings Generated by Their Units |
| |
| 作者姓名： | Huan Yin CHEN |
| |
| 作者单位： | Department of Mathematics, Hunan Normal University, Changsha 410006, P. R. China |
| |
| 基金项目： | Supported by Natural Science Foundation of Hunan Province （04JJ40003） |
| |
| 摘 要： | Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈U（R） such that 1R ± u ∈ U（R）, if and only if for any a ∈ R, there exists a u ∈ U（R） such that a ± u∈ U（R）. Phrthermore, we prove that, for any A ∈ Mn（R）（n ≥ 2）, there exists a U ∈ GLn（R） such that A ± U ∈ GLn（R）.
|
| 关 键 词： | 交换环 强π-正则环 广义线性群 准素因子 |
| 收稿时间： | 18 October 2005 |
| 修稿时间： | 2005-10-182006-03-01 |
Exchange Rings Generated by Their Units |
| |
| Huan Yin CHEN.Exchange Rings Generated by Their Units[J].Acta Mathematica Sinica,2007,23(2):357-364. |
| |
| Authors: | Huan Yin Chen |
| |
| Institution: | (1) Department of Mathematics, Hunan Normal University, Changsha 410006, P. R. China |
| |
| Abstract: | Let R be an exchange ring with primitive factors artinian. We prove that there exists a u∈ U(R) such that 1
R
± u ∈ U(R), if and only if for any a∈ R, there exists a u ∈ U(R) such that a ± u ∈ U(R). Furthermore, we prove that, for any A ∈ M
n
(R)(n ≥ 2), there exists a U ∈ GL
n
(R) such that A ± U ∈ GL
n
(R).
Supported by Natural Science Foundation of Hunan Province (04JJ40003) |
| |
| Keywords: | exchange ring primitive factors artinian strongly p-regular ring |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
