【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.更多还原

【Abstract】 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, semiperfect ring, MI-ring and so on. Main results obtained read as following: （1）Let R be a left AP-injective ring and left duo ring, if it is also a local Baer ring, then it is a left continuous ring; （2）Let R={i∈IR_i} be a left AP-injective ring, in which R_i is an uniform left ideal,if R is a Baer ring and left duo ring,then R is a left continuous ring; （3）Let R be a left AP-injective ring and left duo ring,if R 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.更多还原