Exchange的GCN环  

Exchange GCN rings

作　　者：屈寅春[1,2] 魏俊潮[1] 

机构地区：[1]扬州大学数学科学学院,江苏扬州225002 [2]无锡职业技术学院,江苏无锡214121

出　　处：《扬州大学学报（自然科学版）》2015年第4期13-15,共3页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11471282);江苏省高等职业院校国内高级访问学者计划资助项目(2014FX079)

摘　　要：研究了GCN环的相关性质及应用,并证明了如下结论:1)设R为一个exchange的GCN环,如果R的每个素理想是左本原的,则R为强π-正则环;2)一个环R为强正则环当且仅当R为半素的exchange的GCN环且每个素理想是左本原的;3)完全左幂等的exchange的GCN环是强正则环;4)设R为一个exchange的GCN环,则群环R[G]是von Neumann正则环当且仅当R[G]是完全左幂等环.This paper is a further study of GCN ring. The main results are as follows： 1） Let R be an exchange GCN ring, if every prime ideal of R is left primitive, then R is a strongly π - regular ring; 2） A ring R is a strongly regular ring if and only if R is a semiprime exchange GCN ring and every prime ideal of R is left primitive; 3） Full left idempotent exchange GCN ring is a strongly regular ring; 4） Let R be an exchange GCN ring, group ring R[G] is avon Neumann regular ring if and only if R[G] is a full left idempotent ring.

关 键 词：exchange的GCN环 强正则环 完全左幂等环 左V-环 约化环 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]