σ-半素环上广义（θ，θ）-导子的性质

Properties of Derivationson Generalized（θ,θ）-Derivatives on σ-Semi-prime Rings

运用替换、线性化等代数方法研究将半素环上广义(θ,θ)-导子的性质推广到σ-半素环上.如果R是σ-半素环,θ是R上的自同构,设F是R上的广义(θ,θ)-导子,(θ,θ)-导子d是F的伴随导子,且d与σ都是可交换的.若F在R上作为同态,则有d=0.

By use of the algebraic methods such as substitution and linearization,the properties of the generalized-derivatives on the semi-prime ring were extended to theσ-semi-prime ring.If(θ,θ)Ris aσ-semi-prime ring,andθis an automorphism on R,meanwhile let Fbe a generalized(θ,θ)-derivation on R,-derivative dis an adjoint derivative of F,andσare commutative,if F on Ris of(θ,θ)homomorphism,there is d=0.