素环上的导子

The Derivation of Prime Ring

设R是素环,Qmr是环R的极大右商环,C是Qmr的中心,δ1,δ2,δ3是环R上的非零导子,若l1δ1+l2δ2+l3δ3,li≠0,i=1,2,3仍是环R上的导子,且满足[l1δ1(x)+l2δ2(x)+l3δ3(x),x]=0,x∈R,则可给出导子δ1,δ2,δ3的具体表达式。

Let R be a prime ring with maximal right ring of quotients Qmr ,C is the center of Qmr δ1,δ2,δ3are derivations of R.If l1δ1＋l2δ2＋l3δ3,li≠0,i=1,2,3 is still a derivation of Rang the expression [l1δ1（x）＋l2δ2（x）＋l3δ3（x）,x]=0,x∈R is satisfied , then their specific expressions are given.