三角代数上的非线性(m,n)-高阶导子

Nonlinear(m,n)-Higher Derivations On Triangular Algebras

设m和n是任意固定的非零整数且(m+n)(m-n)≠0,u是一个|mn(m+n)|-无挠的三角代数,D={d_k}_(k∈N)是u上的一个(m,n)-高阶可导映射.本文证明了:三角代数u上的每一个(m,n)-高阶可导映射都是高阶导子.作为结论的应用,得到了套代数或|mn(m+n)|-无挠的上三角分块矩阵代数上的每一个(m,n)-高阶可导映射都是高阶导子.

Let m,n be non-zero integers with （m＋n）（m-n）≠0, U an｜mn（m＋n）｜-torsion free triangular algebra and D={dk}k∈N （m,n）-higher derivable map from U into itself. In this paper, it is shown that every （m,n）-higher derivable map on U is a higher derivation. As its application, we get that every （m,n）-higher derivable map on a nest algebra or an｜mn（m＋n）｜-torsion free block upper triangular matrix algebra is a higher derivation.