广义导子幂中心化子条件

Annihilators of Power Central Values of Generalized Derivations

设R是半素环，U是R的极大右商环，C是R的扩展型心，a，b∈U．对R上广义导子δ的值的幂零，幂中心化子问题进行了讨论，即（aδ（x））^m b=0（∈C）形式的恒等式，对δ的形式以及δ与a，b的关系做了完整的刻画，从而发展了Herstein，Bresar的研究结果．

Let R be a semiprime ring with extended centroid C and maximal right ring of quotients U, a, b ∈ U and δ a generalized derivation of R. This article studies annihilators of nilpotent and power central values of generalized derivations, that is the identity （aδ（x））^nb = 0 （∈ C）, and completely characters δ and the relation between δ and a, b. The results simultaneously generalize some results of Herstein and Bresar.