单位正则环中的零化子(英文)  

Annihilators in Unit-Regular Rings

作　　者：陈焕艮[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《杭州师范大学学报（自然科学版）》2010年第1期1-5,共5页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：Supported by the Natural Science Foundation of Zhejiang Province (Y6090404)

摘　　要：环R称为单位正则环,如果对任何x∈R,有可逆元u∈R使得x=xux.文章利用零化子刻画了单位正则环,证明了正则环是单位正则环当仅当l(a)∩l(b)=l(d)时,有y∈R使得l(a)∩l(b)=l(a+by),当仅当l(a)=l(b)时,有u∈U(R)使得a=bua.A ring R is unit-regular provided that for any x E R, there exists an invertible u E R such that x= xux. The paper has characterized the unit-regular ring by means of annihilators, proved that a regular ring R is unit-regular if and only if whenever t（a）∩t（b）=t（d）, there exists y∈R such that l（a）∩t（b）=t（a＋by）, and if and only if whenever t（a）=t（b）, there exists uE U（R） such that a=bua.

关 键 词：零化子 单位正则环 稳定秩1 

分 类 号：O153[理学—数学]