摘要
设R是中心为Z,扩张形心为C的素环,证明了:设,(x),g(x),h(x)为R上非零导子,若af(x)+bg(x)+ch(x)亦是R上导子,且在R上交换,则f(x)=λ1x+ζ1(x),g(x)=λ2x+ζ2(x),h(x)=λ3x+ζ3(x),其中λ1,λ2,λ 3∈C,ζ1,ζ2,ζ3为R一C的加性映射.
Let R be a prime ring with center Z and extended centroid C , We prove the following results: (1)Let f(x),g(x),h(x) be non-zero derivations in prime rings R , suppose there exist a,b,c∈R such that af(x)+bg(x)+ch(x) is a derivations of R and commuting on it, then f(x)=λ_1x+ζ_1(x),g(x)=(λ_2(x))+ζ_2(x),h(x)=λ_3x+ζ_3(x),λ_1,λ_2,λ_3∈C, additive map ζ_1,ζ_2,ζ_3∶R→C.
出处
《北华大学学报（自然科学版）》
CAS
2004年第3期197-198,共2页
Journal of Beihua University（Natural Science）
关键词
素环
极大右商环
导子
扩张形心
Prime ring
Maximal right ring of quotients
Derivation
Extended centriod
