素环上的交换映射

Commuting mappings in prime rings

设R是一个环,F:R→R是一个映射.如果对所有的x∈R,有[F(x),x]=0成立,则称F是R上的交换映射.文章的主要结论为:设R是特征不为2的素环.如果存在一个非零广义导子:δR→R,使得映射x→[δ(x),x]在R上是可变换的且δ(I)∈Z(R),则δ在R上是可交换的.

Let R be a ring. A mapping F：R→R is said to be commuting on R it IF（x） ,x] =0 holds lot all x R. The main result of this paper is ：let R be a prime ring of characteristic not two. Suppose there exists a nonzero generalized derivation δ ：R→R, such that the mapping x→[ δ（x） x] is commuting on R and δ（I） ∈ Z（R）, then δ is commuting on R. Key words： prime ring,commuting mappings,generalized derivation.