有限结合环类中的特殊根

Special Radical in the Class of all Finite Associative Rings

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.