摘要
设A是Jordan代数,如果映射d:A→A满足任给a,b∈A,都有d(aob)=d(a)o b+aod(b),则称d为可乘Jordan导子.如果A含有一个非平凡幂等p,且A对于p的Peirce分解A=A_1⊕A_(1/2)⊕A_0满足:(1)设ai∈Ai(i=1,0),如果任给t_(1/2)∈A_(1/2),都有a_i○t_(1/2)=0,则a_i=0,则A上的可乘Jordan导子d.如果满足d(p)=0,则d是可加的.由此得到结合代数和三角代数满足一定条件时,其上的任意可乘Jordan导子是可加的.
Let A be a Jordan algebra.If the map d：A→A satisfies d（a o b） = d（a） o b ＋ a o d（b） for all a,b∈A,then d is called a multiplicative Jordan derivation on A.Our main objective in this note is to prove the following.Suppose A has an idempotent p（p≠0,p≠1） which satisfies that the Peirce decomposition of A with respect to p,A = A_1 ？ A_（1/2） ？ A_0,satisfies that （1） Let a_i∈A_i（i =,0）.If a_i o t_（1/2） =0 for all t_（1/2）∈A_（1/2）,then a_i = 0. If d is any multiplicative Jordan derivation of A which satisfies that d（p） = 0,then d is additive.As its application,we get the result that every multiplicative Jordan derivation on some associative algebras and triangular algerbas is additive.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2010年第3期571-578,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10971117
10675086)
山东省基金资助项目(Y2006A04)
