特征不为2的素环可交换的又一条件

THE ANOTHER CONDITION OF MAKING THE PRIWE RING WITH CHARACTERISTIC NOT 2 BE COMMUTATIVE RING

设Ｒ是中心为Ｃ且特征不为２的素环。本文证明了下列结果：Ｎ是Ｒ的非零理想，ｄ是Ｒ上一个非零导子，若对一切ａ∈Ｎ．［ｄ２（ａ），ａ］∈Ｃ则Ｒ是一个交换环。

he purpose of this paper is to prove the following theorem which generalizes both a classical result of E.Posner and a recent result of L.O.chung and Jiang Lug:Let R be a prime ring of characteristic different from 2 and N a nonzero ideal of R,suppose the d is a nonzer derivation. on R such that d2(a)a-ad2(a)is central for all a∈N.Then R is a commutative ring.