关于环的正则性  

On the Regularity of Rings

作　　者：赵良[1] 

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《江西理工大学学报》2007年第3期58-59,共2页Journal of Jiangxi University of Science and Technology

摘　　要：利用环的拟理想对环的正则性进行了刻画,主要得到了两个结果:①设R是左SPF-环.若R的每一个极大的左理想是拟理想,则R/J(R)是强正则环.②设环R的每一个极大的左理想是拟理想,则以下等价:R是强正则环;R是广义正则的SI环;每一个单左R-模是GP-内射的.In this paper, two results on the regularity of rings characterized by their quasi-ideal are mainly obtained： ①If R is a left SPF-ring whose every maximal left ideal is a quasi-ideal,then R/J（R ）is a strongly R is a ring whose every maximal left ideal is a quasi-ideal, then the following regular ring.②If statements are equivalent：R is a strongly regular ring. R is a generalized regular SI ring. Every simple left R -module is GP-injective.

关 键 词：正则环 拟理想 SPF-环 

分 类 号：O153.3[理学—数学]