Some Results about Derivations of Prime Rings

Abstract:

      Let R be a 2-torsion free noncommutative prime ring and d be a derivation of R. If [x^d, x]x^d = 0 for all x ∈ R, then d = 0. Furthermore, if [[x^d, x],x^d] = 0 for all x ∈ R, then d=0.