三角代数上的零点(m,n)-高阶可导映射

(m,n)-higher derivable mappings of triangular algebras at zero point

用矩阵分解的方法证明了|mn(m+n)(m-n)|-无挠的三角代数上的每一个零点(m,n)-高阶可导映射都是高阶导子。作为此结论的应用,得到套代数或|mn(m+n)(m-n)|-无挠的上三角分块矩阵代数上的每一个零点(m,n)-高阶可导映射都是高阶导子。

The method of decomposing matrix is used.It is shown that every zero point (m,n)-higher derivable map on a|mn(m+n)(m-n)|-torsion free triangular algebra is a higher deriva-tion.As its application,it is proved that every zero point (m,n)-higher derivable map on a nest al-gebra or a|mn(m+n)(m-n)|-torsion free block upper triangular matrix algebra is a higher deri-vation.