三角代数上Lie积为平方零元的非线性双可导映射

设U是一个三角代数，Ω是U上平方零元的集合，φ：U×U→U是U上的一个映射(在每个变量上都没可加假设).若对任意的x，y，z∈U且x，y]，y，z]∈Ω分别有φ(xy，z)＝φ(x，z)y＋xφ(y，z)和φ(x，yz)＝φ(x，y)z＋yφ(x，z)，则φ是U上的一个双导子.

Nonlinear biderivable maps on triangular algebras by Lie product square zero elements

Let U be a triangular algebra and Ω be the set of square zero elements of U，φU×U→U be a mapping on U(without assumption of additivity on each argument). In this paper， we show that if φ satisfies φ(xy，z)＝φ(x，z)y＋xφ(y，z) and φ(x，yz)＝φ(x，y)z＋yφ(x，z) for all x，y，z∈U with x，y]，y，z]∈Ω， then φ is a biderivation.