| 三角代数上Lie积为平方零元的非线性Jordan高阶可导映射 |
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| 引用本文： | 费秀海,戴磊,朱国卫. 三角代数上Lie积为平方零元的非线性Jordan高阶可导映射[J]. 山东大学学报(理学版), 2019, 54(12): 50-58. DOI: 10.6040/j.issn.1671-9352.0.2019.100 |
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| 作者姓名： | 费秀海 戴磊 朱国卫 |
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| 作者单位： | 1. 滇西科技师范学院数理学院, 云南 临沧 677099;2. 渭南师范学院数学与统计学院, 陕西 渭南 714099 |
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| 摘 要： | 设U是一个 2-无挠的三角代数,D ={dn}n∈N是U上一个Lie积为平方零元的非线性Jordan高阶可导映射。证明了三角代数U上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。作为结论的应用,得到套代数或 2-无挠的上三角分块矩阵代数上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。
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| 关 键 词： | 三角代数 高阶导子 Jordan 高阶导子 平方零元 |
Nonlinear Jordan higher derivable maps on triangular algebras by Lie product square zero elements |
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| FEI Xiu-hai,DAI Lei,ZHU Guo-wei. Nonlinear Jordan higher derivable maps on triangular algebras by Lie product square zero elements[J]. Journal of Shandong University, 2019, 54(12): 50-58. DOI: 10.6040/j.issn.1671-9352.0.2019.100 |
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| Authors: | FEI Xiu-hai DAI Lei ZHU Guo-wei |
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| Affiliation: | 1. School of Mathematics and Physics, Dianxi Science and Technology Normal University, Lincang 677099, Yunnan, China;2. School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China |
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| Abstract: | Let U be a 2-torsion free triangular algebra, D={dn}n∈N is a nonlinear Jordan higher derivable map on triangular algebra U by Lie product square zero elements. In this paper, it is shown that every nonlinear Jordan higher derivable map on triangular algebra U by Lie product square zero elements is a higher derivation. As its application, we get that every nonlinear Jordan higher derivable map on a nest algebra or a 2-torsion free block upper triangular matrix algebra U by Lie product square zero elements is a higher derivation. |
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| Keywords: | triangular algebra higher derivation Jordan higher derivation square zero element |
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