GP-V环和SF环的正则性  

Regularity of GP-V-rings and SF-rings

作　　者：李刘文[1] 肖光世[1] 

机构地区：[1]南京航空航天大学理学院,江苏南京210016

出　　处：《成都信息工程学院学报》2007年第6期776-779,共4页Journal of Chengdu University of Information Technology

摘　　要：主要讨论GP-V环和SF环的正则性,得到如下结果:(1)如果R是左GP-V′环且R的每一补左理想是理想,那么R是约化的双正则环;(2)R是强正则环当且仅当每一单奇异左R-模是平坦的且R的任意元素a满足r(a)l(a);(3)如果R是左SGPF环且R的每一极大左理想是弱右理想,那么R/J(R)是强正则环.The regularity of GP-V-rings and SF-rings is discussed and the following results are obtained： （1） If R is a left GP-V＇ ring and every complement left ideal of R is an ideal, then R is a reduced biregular ring; （2） R is strongly regular if and only if every simple singular left R-module is flat and every a in R satisfies r （a）lohtatn in I （a）, （3） If R is a left SGPF ring and every maximal left ideal is a weakly right ideal, then R/J（R） is a strongly regular ring.

关 键 词：GP-V环 SF环 正则环 

分 类 号：O153.3[理学—数学]