素环上的广义(θ,θ)-导子

Generalized (θ,θ)-derivations in a 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上的广义(θ,θ)-导子,(θ,θ)-导子d是F的伴随导子,有F(xy)=F(x)F(y)或F(xy)=F(y)F(x),x,y∈I.若d≠0,则R为可交换的.

In the present paper it is shown that: if R is 2 - torsion free prime ring,let I be a nonzero ideal of R ,θ an automorphism of R and F a generalized ( θ,θ) - derivation of R such that eitherF( xy) = F( x)F( y) or F( xy) = F( ) y F( ) x for allx,y ∈ I ,if d≠0,then R is commutative.