Engel-Type Conditions Involving Two Generalized Skew Derivations in Prime Rings

Abstract

Let ℛ be a prime ring of characteristic different from 2, 𝒬r the right Martindale quotient ring of ℛ, 𝒞 the extended centroid of ℛ, F, G two generalized skew derivations of ℛ, and k ≥ 1 be a fixed integer. If [F(r), r]kr − r[G(r), r]k = 0 for all r ∈ ℛ, then there exist a ∈ 𝒬r and λ ∈ 𝒞 such that F(x) = xa and G(x) = (a + λ)x, for all x ∈ ℛ.