Annihilators of power values of derivations on Lie ideals of prime rings

摘要

Let R be a prime ring with the extended centroid C and L a noncentral Lie ideal of R. Suppose that a∈R, γ∈C and d is a derivation of R such that ad(u2)s−γu2tm∈C for all u∈L, where s,t,m are fixed positive integers. If γ≠0 or d≠0, then a=0 unless R⊆M2(F), the 2×2 matrix ring over a field F. This result gives an affirmative answer to the open conjecture recently raised by Huang in [Derivations with annihilator conditions on Lie ideals in prime rings, J. Algebra Appl. 19 (2020) 2050025].