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

摘要

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 is an element of L, where k >= 1 is a fixed positive integer.