关于素环的导子

ON DERIVATIONS OF PRIME RINGS

设Ｒ是一个中心为Ｃ的素环，Ｎ是Ｒ的一全非零理想。本文我们将证明下列结果：假设Ｄ是Ｒ的一个非零导子使得对或者对一切ａ∈Ｎ，那么当Ｒ的特征不等于２时，Ｒ是一个交换环。我们的结果推广了文献［２］，［４］，［８］中有关素环导子的某些已知结果。

Let R be a prime ring with center C and N a nonzero ideal ofR.Our main purpose here is to prove the following results: Suppose d isnonzero derivation on R such that either d￣2(a￣2)∈C for all α∈N or[d(a),a￣2]∈C for all α∈N,then R is a commutative ring when R is of characteristicnot 2.Our results generalizc some well-known results in[2],[4],[8]。