摘要
通过单边理想是广义弱理想来刻画强正则环,证明了下列条件是等价的①R是强正则环;②R是Abelian的左GPV′环,且每一个极大的本质的左理想是广义弱理想;③R是Abelian的左GPV′环,且每一个极大的右理想是广义弱理想.并证明了若R是左GPV′环,则Z(RR)∩J(R)=0;Z(RR)∩Z(RR)=0.
In this paper, the authors characterize extensively regular rings via generalized weakly ideals. The following conditions are shown to be equivalent： （1）R is a strongly regular ring,（2）R is an Abelian left GP - V′-ring whose every essential maximal left ideal is a generalized weakly ideal, （3）R is an Abelian left GP - V′- ring whose every maximal right ideal is a generalized weakly ideal, and also prove if R is a left GP- V′- ring then Z（RR）∩（R）=0;Z（RR）∩（RR）=0.
出处
《湖州师范学院学报》
2006年第2期23-26,共4页
Journal of Huzhou University
基金
安徽师范大学专项科学基金资助项目(2005BZX18).
