Annihilators of power values of derivations in prime rings

Abstract

In this paper we prove some results concerning annihilators of power values of derivations in prime rings. The following main theorem establishes a unified version of several earlier results in the literature:Let R be a prime ring with center Z and with extended centroid C,Q, its two-sided Martindale quotient ring, ρ a nonzero right ideal of R and D a nonzero derivation of R.Suppose that aD([x,y])n ∈ Z (D([x,y])na ∈ Z) for all x,y∈ρ where a∈Rand n is a fixed positive integer. If [ρ,ρ]ρ ≠ 0 and dim C RC >4, then either aD(ρ) = 0 (a = 0 resp.) or D= ad(p) for some p∈ Qsuch that pρ = 0.