Abstract:

Let A and B be Jordan algebra. The bijection :A→B is called a Jordan triple map, if (｛abc｝)=｛(a)(b)(c)｝[JP] for all a,b,c∈A. IfA　contains a nontrivial idempotent p, and the Peirce decomposition A=A₁A₁₂,A₀  of  A with respect to p, and satisfies that(1) ai∈Ai(i=1,0), if ait₁₂=0 for all t₁₂∈A12, then   a _i=0, every Jordan triple map from A onto B is additive.

Key words: Jordan algebra; Jordan triple map; additivity