摘要
设Ω是有限结合环类中全部弱单环组成的环类,Ω1∪Ω2=Ω,Ω1∩Ω2=Φ,在有限结合环类中,我们证明了LΩ1=UΩ2可以成立,并给出等式成立的充要条件.使用这个结论,我们可以证明,在有限结合环类中,超幂零根是特殊根.
In the class of all finite associative rings,let Ω be a class of all weak simple rings,Ω1∪Ω2=Ω,Ω1∩Ω2=Φ. Let P be a class of all rings of order pn,n≥0,p a prime number. p0 a nilpotent ring of order p. It is proved that LΩ1= UΩ2,iff Ω1∩P=Φ,or p0∈Ω1∩P for all p. Therefore we can prove that every supernilootent radical is special.
出处
《数学研究》
CSCD
1996年第2期86-87,共2页
Journal of Mathematical Study