素环上的左(θ,θ)-导子

Left (θ, θ)-derivations in the prime Ring

R为2-扭自由素环,I为R的非零理想,θ是R上的自同构,F是R上的左(θ,θ)-导子,有F(xy)=F(x)F(y)或F(xy)=F(y)F(x),?x,y∈I.若F≠0,则R为可交换的.

If R is a 2-torsion free prime ring, I a nonzero ideal of R,θ an automorphism of R, F a left (θ,θ)-derivation of R, and F(xy)=F(x)F(y) or F(xy)=F(y)F(x), x, y∈I. if F≠0, then R is commutative.