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

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 a d (u 2) s − γ u 2 t m ∈ C for all u ∈ L , where s , t , m are fixed positive integers. If γ ≠ 0 or d ≠ 0 , then a = 0 unless R ⊆ M 2 (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]. [ABSTRACT FROM AUTHOR]