Lie ideals and Jordan generalized \((\theta,\varphi)\)-derivations of prime rings. (Q875661)

Let \(R\) be a prime ring with \(\text{char\,}R\neq 2\), and let \(U\) be a Lie ideal of \(R\) so that \(u^2\in U\) for all \(u\in U\). The main result proves that if \(F\colon R\to R\) is additive and acts on \(U\) like a Jordan generalized \((\theta,\varphi)\)-derivation, for \(\theta\) and \(\varphi\) automorphisms of \(R\), then \(F\) acts on \(U\) like a generalized \((\theta,\varphi)\)-derivation.