Let R be a prime ring of characteristic different from 2 and 3,Qr be its right Martindale quotient ring and C be its extended centroid.Suppose that F and G are generalized skew derivations of R,L a non-central Lie ide...Let R be a prime ring of characteristic different from 2 and 3,Qr be its right Martindale quotient ring and C be its extended centroid.Suppose that F and G are generalized skew derivations of R,L a non-central Lie ideal of R and n≥1 a fixed positive integer.Under appropriate conditions we prove that if(F(x)x;—xG(x))^n=0 for all x∈L,then one of the following holds:(a)there exists c∈Qr such that F(x)=xc and G(e)=cx;(b)R satisfies S4 and there exist a,b,c∈Qr such that F(x)=ax+xc,G(x)=cx+xb and(a—b)^2=0.展开更多
文摘Let R be a prime ring of characteristic different from 2 and 3,Qr be its right Martindale quotient ring and C be its extended centroid.Suppose that F and G are generalized skew derivations of R,L a non-central Lie ideal of R and n≥1 a fixed positive integer.Under appropriate conditions we prove that if(F(x)x;—xG(x))^n=0 for all x∈L,then one of the following holds:(a)there exists c∈Qr such that F(x)=xc and G(e)=cx;(b)R satisfies S4 and there exist a,b,c∈Qr such that F(x)=ax+xc,G(x)=cx+xb and(a—b)^2=0.
