Nonlinear biderivable maps on triangular algebras by Lie product square zero elements
FEI Xiuhai1， DAI Lei2， ZHANG Haifang1
1.School of Mathematics and Physics， Dianxi Science and Technology Normal University， Lincang， Yunnan 677099， China； 2.College of Mathematics and Information Science， Weinan Normal University， Weinan， Shaanxi 714099， China
Abstract：Let U be a triangular algebra and Ω be the set of square zero elements of U，φ：U×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.
2021, Vol. 55 
