| 广义矩阵代数上一类非全局非线性三重高阶可导映射 |
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| 引用本文： | 费秀海,张海芳. 广义矩阵代数上一类非全局非线性三重高阶可导映射[J]. 山东大学学报(理学版), 2022, 57(10): 97-105. DOI: 10.6040/j.issn.1671-9352.0.2021.247 |
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| 作者姓名： | 费秀海 张海芳 |
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| 作者单位： | 滇西科技师范学院数理学院, 云南 临沧 677099 |
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| 基金项目： | 国家自然科学基金资助项目(11901248);云南省教育厅基础研究基金资助项目(2022J1014);云南省2021年学术和技术后备带头人才资助项目(202105AC160089) |
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| 摘 要： | 设G是一个满足MN=0=NM的2-无挠的广义矩阵代数,Q={A∈G:A2=0},D={dn}n∈N是G上一列映射(没有可加性假设)。文章证明:若对任意n∈N,A,B,C∈G且ABC∈Q,有dn(ABC)=∑r+s+t=ndr(A)ds(B)dt(C),则D是一个可加的高阶导子。作为应用,在三角代数上得到了相同的结论。
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| 关 键 词： | 广义矩阵代数 三重高阶可导映射 高阶导子 |
A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras |
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| FEI Xiu-hai,ZHANG Hai-fang. A class of non-global nonlinear triple higher derivable maps on generalized matrix algebras[J]. Journal of Shandong University, 2022, 57(10): 97-105. DOI: 10.6040/j.issn.1671-9352.0.2021.247 |
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| Authors: | FEI Xiu-hai ZHANG Hai-fang |
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| Affiliation: | School of Mathematics and Physics, West Yunnan University, Lincang 677099, Yunnan, China |
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| Abstract: | Let G be a 2-torsion free generalized matrix algebra with MN=0=NM,Q={A∈G:A2=0} and D={dn}n∈N be a sequence mapping from G into itself(without assumption of additivity). In this paper, it is shown that if D satisfies dn(ABC)=∑r+s+t=ndr(A)ds(B)dt(C)for all n∈N,A,B,C∈G with ABC∈Q, then D is an additive higher derivation. As its applications get that the similar conclusion on Triangular algebras. |
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| Keywords: | generalized matrix algebra triple higher derivable map higher derivation |
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