准正则环与正则环  

ON QUASI-REGULAR AND REGULAR RINGS

作　　者：胡先惠[1] 

机构地区：[1]中央民族学院

出　　处：《数学杂志》1994年第4期519-522,共4页Journal of Mathematics

摘　　要：每一个主左理想均由一个幂等元生成的环叫正则环。每一个左理想均山若干个幂等元生成的环叫准正则环。本文研究准正则环与正则环的一些性质，讨论准正则环成为正则环的一些条件，准正则环、正则环与Ｖ环之间的关系，准正则环成为Ａｂｅｌ正则环的条件。A associative ring R is called a regular ring if every left principle ideal of it is generated by an idempotent.R is called a quasi-regular,if every principle left ideal of it is generated by some idempotents. in this paper,we study the property of quasi-regular ring,and consider the condition that a quasi-regular ring beccme regular ring,we study the relation between quasi-regular ring and V一ring, and consider the condition that a quasi-regular become abelian regular.

关 键 词：正则环 准正则环 V环 阿贝尔正则环 

分 类 号：O153.3[理学—数学]