三角代数上的可乘导子

Multiplicative Derivations of Triangular Algerbas

设T是环R上的三角代数,研究三角代数T上的可乘导子的可加性。利用矩阵分块理论证明了满足一定条件的三角代数上的每一个可乘导子是可加的,从而得到套代数中许多标准子代数上的可乘导子是可加的。

Let T be a triangular algebra on a ring R. The multiplicative derivation of triangular algebra is considered. Using the theory of partisioning,the additivity of multiplicative derivation of T satisfying some conditions is proved. Consequently,every multiplicative derivation of some standard subalgebras of nest algebras is additive.