关于上三角矩阵代数上的导子系

Derivation systems on upper triangular matrix algebra

设U=Tri(A,M,B)是上三角矩阵代数。利用算子论的方法讨论了上三角矩阵代数上的Jordan导子系,证明了上三角矩阵代数上的Jordan导子系都是上三角矩阵代数上的导子系,从而给出上三角代数上Jordan导子系的一种新的刻画。

Let U=Tri（A,M,B） be a triangular algebra.In this paper,By using of operator theory methods,it is proved that every Jordan derivation system on upper triangular matrix algebra U is a derivation system on upper triangle matrix algebra U,the notion of Jordan higher order derivations on upper triangle matrix algebra U to a more general case is generalized.