An Engel condition with X-generalized skew derivations on Lie ideals

Motivated by Kosan and Lee’s elegant paper and Liu’s systematic works, this article is targeted towards the Engel conditions with X-generalize skew derivations on Lie ideals. Let R be a prime ring of characteristic different from 2, Q _r be its right Martindale quotient ring and C be its extended centroid, F an X-generalized skew derivation of R, L a non-central Lie ideal of R. Then, we describe all possible forms of F satisfying the condition (F(u) u] _k = 0 for all u ∈ L, where k ≤ 1 is a fixed positive integer.