AP-内射环的某些研究  

A NOTE ON AP-INJECTIVE RINGS

作　　者：肖光世[1] 储茂权[2] 

机构地区：[1]南京大学数学系,江苏南京210008 [2]安徽师范大学数学与计算机学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2001年第3期210-213,共4页Journal of Anhui Normal University(Natural Science)

摘　　要：主要目的是借助P -内射环上的一些性质研究AP -内射环的一些性质及其在AGP -内射环上的推广 .(1)设R为无挠右AP -内射环 ,且对于任意a∈R ,有aR =Ra ,则R的每个理想均有唯一极大本质扩张 .(2 )设R是非奇异左AP -内射环 ,且对任意a∈R ,有Ra =aR .如果是右duo环 ,那么R是右有限维数环当且仅当R仅有有限个极大左理想 ,且b(R)是右有限维的 .The purpose of this paper is to study some properties of AP-injective rings and generalizations in AGP-injective rings by some properties of P-injective rings. (1) Let R be a torsion free right AP-injective ring. If aR=Ra for any a∈R, then every ideal of R only has a maximal essential extension. (2) Let R be a nonsingular left AP-injective ring with aR=Ra for any a∈R. If R is right duo ring, then R is right finite-dimensional if and only if R only have finite maximal left ideal and b(R) is right finite-dimensional.

关 键 词：AP-内射环 GPP-环 Π-正则环 duo-环 AGP-内射环 唯一极大本质扩张 极大左理想 

分 类 号：O153.3[理学—数学]