Brear定理的推广  

A generalizaion of Bre■ar's theorem

作　　者：杨弘[1] 

机构地区：[1]湖北大学商学院,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2004年第4期277-278,共2页Journal of Hubei University：Natural Science

摘　　要：MaterfBre ar在1993年得出,如果R是素环,F:R→R是非零的中心化可加映射,当R特征不同于2或F在R上交换,则F(x)=λx+ξ(x)对所有x∈R都成立,其中λ∈C(R的扩张形心),ξ:R→C是一可加映射.证明了将F的象集从R扩大到Q(R的极大右商环)时,仍有类似的结论.Brear obtained a conclusion in 1993:Let R be a prime ring. Suppose an additive mapping F of R into itself is centralizing on R. If either R has a characteristic different from 2 or F is commuting on R, then F is of the form F(x)=λx+ξ(x),x∈R, where λ is an element from the extended controid C of R and ξ is an additive mapping of R into C. In the note will verify:F:R→R can be expansed to F:R→Q, there is still the similar conclusion.

关 键 词：极大右商环 扩张形心 类似 素环 象集 定理 映射 证明 结论 推广 

分 类 号：O153.3[理学—数学] G633[理学—基础数学]