| Abstrakt: |
Let Rbe any non-commutative prime ring of char (R)≠2, La non-central Lie ideal of Rand F, Gbe b-generalized skew derivations of R. Suppose that [F(u)u-uG(u),u]n=0for all u∈Land for some fixed integer n≥1, then one of the following assertions holds: there exist a′′,b′′∈Qrsuch that F(x)=xa′′, G(x)=b′′xfor all x∈Rwith a′′-b′′∈C;R⊆M2(K),the algebra of 2×2matrices over a field Kandeither Kis a finite field;or there exists λ∈Csuch that (F+G)(x)=λxfor all x∈R;or there exists λ∈Cand h∈Qrsuch that (F+G)(x)=hx+xh+λxfor all x∈R.The above result, naturally improves the recent result obtained by Carini et al. in [4]. |
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