零积决定的三角代数

ZERO PRODUCT DETERMINED TRIANGULAR ALGEBRAS

本文研究了三角代数是否是零积决定的代数的问题.利用零积决定的代数的等价条件和代数方法,获得了三角代数是零积决定的代数的条件,推广了矩阵代数是零积决定的代数的结果.作为应用,得到零积决定的代数的零积导子一定是准导子.

This paper researches by algebraic methods whether the triangular algebra is the zero （resp., Lie, Jordan） product determined algebra and obtains that △ is a zero （resp., Lie, Jordan） product determined algebra if A and B are zero （resp., Lie, Jordan） product determined algebras. It generalizes the results that matrix algebra is zero product determined algebra. Applying these we show that zero product derivations of △ are quasi-derivations.