三角代数上的广义高阶Jordan导子

Generalized higher Jordan derivations of triangular algebras

设F=(fi)i∈N是环R上的一族可加映射,如果a,b∈R且存在一个高阶导子D=(di)i∈N,有fn(ab)=∑i+j=nfi(a)dj(b),则称F是一个广义高阶导子;如果存在一个高阶Jordan导子D=(di)i∈N,有fn(a2)=∑i+j=nfi(a)dj(a),则称F是一个广义高阶Jordan导子.证明了三角代数上的每一个广义高阶Jordan导子是广义高阶导子.

Let F=（fi）i∈N be a family of additive mappings of R.It is said that F is a generalized higher derivation if there exists a higher derivation D=（di）i∈N such that fn（ab）=∑i＋j=nfi（a）dj（b） for all a,b∈R.It is said that F is a generalized higher Jordan derivation if there exists a higher Jordan derivation D=（di）i∈N such that fn（a2）=∑i＋j=nfi（a）dj（a）.It is proved that every generalized higher Jordan derivation of triangular algebras is a generalized higher derivation.