Abstract:

 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  xs［d(x),x］kxt=0 for all x∈L, where s,k,t ≥0 are fixed integers. Then char(R)=2. Moreover, if either s=0 or t=0, then RM2(F) for a field F.

Key words: derivation, Engle condition, Lie ideal, prime ring