素环上的导子的性质

The Property in Pprime Ring with Derivations

讨论素环李理想上的导子的性质.设R是特征不为2的素环,U为R的满足对任意u∈U,u2∈U的Lie理想.如果R中存在非零导子d使d(u2)■Z或[d(u),u2]■Z,对任意u∈U,则U■Z.

In this paper, we discuss the property of iderls in prime ring with derivations. Let R be a prime ring of Char R ≠ 2 and let U be a Lie iderl of R , that is satisfied u2 ∈ U for all u ∈ U . if there exists a nonzero derivation d in R such that d（u2） （∩→）Z or[d（u）,u2]（∩→）Z or all u ∈ U, then U （∩→） Z.