AP-内射环与正则环  

AP-INJECTIVE RINGS AND REGULAR RINGS

作　　者：肖光世[1] 

机构地区：[1]安徽师范大学数学计算机学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2000年第4期399-400,404,共3页Journal of Anhui Normal University(Natural Science)

基　　金：安徽师范大学青年科研基金资助项目

摘　　要：本文的主要目的是给出右AP 内射环与正则环的一些联系以及AP 内射环满足一定条件下是VonNeumann正则环 .( 1)设R是非奇异右AP 内射环 .如果R满足WSRA升链条件 ,那么R是正则环 .( 2 )如果R是非奇异右AP 内射环 ,且满足右有限维数 ,那么R是正则环 .( 3)设R是右AP 内射环 ,如果R是约化环 ,那么R是强正则环 .The mainly aim of this paper are to give some connections between right AP-injective rings and regular rings and to study AP-injective rings are Von Neumann regular rings under some conditions. (1) Let R be nonsingular ringt AP-injective ring. If R satisfies WSPA ascending chains conditions, then R is regular ring. (2) If R is nonsingular ringt AP-injective ring with right finite dimensions, then R is regular ring. (3) Let R be nonsingular right AP-injective ring. If R is reduced, then R is regular ring.

关 键 词：AP-内射环 WSRA升链条件 强正侧环 非奇异环 

分 类 号：O153.3[理学—数学]