广义反导子

Generalized antiderivation on upper triangule matrix algebras

设A是一个含单位元I的代数,M表示A的又模,若δ是A到M的线性映射,且a,b∈A,都有(δab)=(δb)a+bδ(a)-bδ(I)a,则称δ是广义反导子.证明了当m≥n时,从上三角矩阵代数Tn到其双模Mm上不存在真的广义反导子.

Let A be an algebra with identity I, and let M denote bimodule of A. A linear map δ： A→M is called generalization antiderivation if δ（ab）=δ（b）a＋bδ（a）-bδ（I）a, for all a, b∈A. In this paper, it is shown that if m≥n, then there is no proper generalized antiderivation from upper triangular algebra Tn into its bimodule Mm.