AP-内射环与连续环  

AP-injective rings and continuous rings

作　　者：杨春兰[1] 陈淼森[1] 

机构地区：[1]浙江师范大学数理学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2005年第3期250-253,共4页Journal of Zhejiang Normal University:Natural Sciences

基　　金：浙江省自然科学基金资助项目(Y604015)

摘　　要：主要研究了AP-内射环成为连续环的条件.在AP-内射环满足C2条件的基础上,结合Baer环、duo环、半完全环、MI环等,探索了何时AP-内射环也满足C1条件,从而成为连续环,得到了一些相关结果:(1)设R是左AP-内射、左duo环,若R又是局部Baer环,则R是左连续环;(2)设R=i∈IRi是左AP-内射环,其中Ri是一致左理想,若R是Baer环且左duo,则R是左连续环;(3)设R是左AP-内射、左duo环,若R又是半完全的Baer环,则R是左连续环;(4)设R是左AP-内射环,RR是弱内射的,则R是左连续环;(5)设R是左AP-内射、左MI环,则R是左连续环.It is aimed to find out conditions of an AP-injective ring to be continuous. Based on the fact that an AP-injective ring satisfies the C2 condition, conditions for an AP-injective ring to satisfy C1 condition were found, then its continuity was deduced by combining with Baer ring, duo ring, semi- perfect ring, MI-ring and so on. Main results obtained read as following： （1）Let R be a left AP-injectire ring and left duo ring, if it is also a local Baer ring, then it is a left continuous ring; （2）Let R=＋i∈IRi be a left AP-injective ring, in which Ri is an uniform left ideal,if R is a Baer ring and left duo ring,thenR is a left continuous ring; （3）Let R be a left AP-injective ring and left duo ring,ifR is a semiperfect Baer ring,then R is a left continuous ring; （4）Let R be a left AP-injective ring, if RR is weak injective, then R is a left continuous ring; （5）Let R be a left AP-injective ring and left MI-ring, then R is a left continuous ring.

关 键 词：AP-内射环 BAER环 duo环 连续环 

分 类 号：O153.3[理学—数学]