微商共同作用在半素环的Lie理想上的结果

本文讨论了微商共同作用在半素环的某个Ｌｉｅ理想上的问题。给出了如下结果：设Ｒ是带有中心Ｚ（Ｒ）的半素环，Ｑｍｒ是Ｒ的极大右商环，Ｌ是Ｒ的非交换Ｌｉｅ理想，ｄ和δ是Ｒ的微商，假设ｒＲ（「Ｌ，Ｌ」）＝０且ｄ（ｘ）ｘ－ｘδ（ｘ）∈Ｚ（Ｒ）对任意ｘ∈Ｌ成立，则在Ｒ的扩张形心Ｃ中存在一个幂等元ｅ使得ｄ（１－ｅ）Ｑｍｒ＝０和δ（１－ｅ）Ｑｍｒ）＝０并且ｅＱｍｒ满足Ｓ４。另外给出微商共同作用在半素环上多项式的结

Derivations Cocentralizing Lie Ideal in Semiprime Rings

Let R be a semiprime ring with center Z(R),Qmr be the maximal right quotient ring of R,d and δ be the derivations of R,L be a noncommuting Lie ideal of R. Suppose that rR([L,L])=0 and d(x)x-xδ(x)∈Z(R) for all x∈L. Then there exists a idempotent e in the extended centroid of R such that d and δ induce zero derivations on (1-e)Qmr and eQmr satisfies S4. Finally we will give a theorem about derivations cocentralizeing multilinear polynomial in semiprime ring.