GWCN环的一些研究  

On GWCN Rings

作　　者：张子珩[1] 储茂权[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2016年第6期530-534,共5页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(11401009)

摘　　要：本文主要讨论了GWCN环的若干性质以及它与一些特殊环的关系,研究了GWCN环的强正则性,证明了:若R是有Abelian极大左理想的GWCN环,那么下列条件等价:(1)R是强正则环;(2)R为左GP-V’-环,且R的极大本质左理想均为广义弱理想;(3)R是左GP-V’-环,且R的极大本质右理想均为广义弱理想.In this paper, we give some properties of GWCN rings and the relationships between GWCN rings and other special rings. The strong regularity of GWCN rings is studied. We mainly obtain that if R has an Abelian maximal left ideal and R is a GWCN ring, then R is strongly regular if and only if R is a left GP-V＇-ring whose maximal essential left ideals are GW-ideals if and only if R is a left GP-V＇-ring whose maximal essential right ideals are GW-ideals.

关 键 词：GWCN环 约化环 弱半交换环 强正则环 

分 类 号：O153.3[理学—数学]