Exchange Rings Generated by Their Units  

作　　者：Huan Yin CHEN 

机构地区：[1]Department of Mathematics,Hunan Normal University

出　　处：《Acta Mathematica Sinica,English Series》2007年第2期357-364,共8页数学学报（英文版）

基　　金：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）.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：exchange ring primitive factors artinian strongly π-regular ring 

分 类 号：O153.3[理学—数学]