关于强正则环的几个等价刻划  

Some Characterizations on Strongly Regular Rings

作　　者：方茵[1] 雷震[2] 

机构地区：[1]芜湖市职教中心,安徽芜湖241000 [2]芜湖师范专科学校数学系,安徽芜湖241008

出　　处：《洛阳师范学院学报》2004年第2期20-21,共2页Journal of Luoyang Normal University

摘　　要：设R是一个环 ,如果对于任意的x ,y∈R ,有xy -yx∈C(R) ,那么下列条件等价 :( 1 )R是强正则环 ;( 2 )R是VonNeumann正则环 ;( 3)R是广义正则环 .设R是半可换环 ,则以下条件等价 :( 1 )R是强正则环 ;( 2 )R的每一个极大的本质的左理想是左GP -内射模 ;( 3)R的每一个极大的本质的右理想是右GP -内射模 .Let R is a ring,if xy-yx∈C(R),for all x,y∈R,then following statements are equivalent: (1)R is a strongly regular ring,(2)R is a Von Neumann regular ring,(3)R is a generalized regular ring;Let R is a semi commutative ring,then following statements are equivalent:(1)R is a strongly regular ring,(2)Every maximal essential left ideals of R are left GP-injective modules,(3)Every maximal essential right ideals of R are right GP-injective modules.

关 键 词：强正则环 正则环 广义正则环 半可换环 GP-内射模 

分 类 号：O153[理学—数学]