素环上具有广义Engel条件的导子

Derivations with Generalized Engel Condition in Prime Rings

利用素环上的微分恒等式研究素环上具有广义Engel条件的导子的性质,得到如下结果:设R是素环,L是R的非中心Lie理想,d是R上的非零导子.若xs[d(x),x]kxt=0,x∈L,其中s,k,t≥0是给定的整数,则char(R)=2.进一步,如果s=0或t=0,则R■M2(F),这里M2(F)表示特征为2的域F上的2阶全矩阵代数.

We investigated derivations with generalized Engel conditions in prime rings applying the theory of differential identities in prime rings. The main result is as follows. Let R be a prime ring, L a noncentral Lie ideal of R, d a nonzero derivation of R. Suppose that x＇[d（x） ,x]kx＇ =0 for all x eL, where s,k,t 〉10 are fixed integers. Then char（R） =2. Moreover, if either s =0 or t =0, then RC_M2（F） for a field F.