对σ-素环上广义导子性质的研究

Study on the properties of generalized derivations on prime ring

设R是2-扭自由σ-素环,I是R的非零σ-理想,设F,G是R的广义导子,d,g是它们的伴随导子,且与σ可交换,若F(x■y)=F(x)■y-d(y)■x,x,y∈I,则R是可交换的.用代数的交换性讨论了广义导子在σ-素环上的性质,并将素环上广义导子推广到σ-素环上.

Let R be a 2-torsion freeσ-prime ring,I be a non-zeroσ-ideal of R,F and G be generalized derivations of R and d and g be adjoint derivations of them,which are commutative withσ.If F(x■y)=F(x)■y-d(y)■x,,for all x,y∈I,then R is commutative.In this paper,we discuss the properties of generalized derivations over prime rings and generalize the generalized derivations over prime rings toσ-prime rings.