关于素环的一个定理

A THEOREM ON PRIME RINGS

设Ｒ是ｃｈａｒＲ≠２，３的非交换素环，Ｄ：Ｒ×Ｒ→Ｒ是非零对称可导的，ｄ是Ｄ的迹，设存在Ｒ的一个同态ｆ，使得ｄ（ｘ）·ｆ（ｘ）＝０对所有ｘ∈Ｒ。

Let R be a non commutative prime ring of char R ≠2,3, let D (·,·): R × R → R and d be a non zero symmetric derivation and the trace of D , respectively, if there is a homomorphism f of R such that d ( x ) f ( x )=0, for all x ∈ R , then f =0.