On a Functional Identity Involving Power Values of Generalized Skew Derivations on Lie Ideals

Let R be a prime ring, Qr its right Martindale quotient ring and C its extended centroid. Suppose that F is a generalized skew derivation of R, L a non-central Lie ideal of R, m,n,s≥1 positive fixed integers. If F(u)n(F(u)m-um)s=0for all u∈L, then there exists λ∈C such that F(x)=λx, for any x∈R, with λm=1, unless when char(R)=2 and R⊆M2(K), the ring of 2×2 matrices over a field K. We will also provide a generalization of the previous result for semiprime rings. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.