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浙江大学学报（理学版）
浙江大学学报（理学版）  2020, Vol. 47 Issue (2): 167-171    DOI: 10.3785/j.issn.1008-9497.2020.02.006
数学与计算机科学     
广义矩阵代数上的一类局部非线性三重可导映射
费秀海1, 戴磊2, 朱国卫1
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
A class of local nonlinear triple derivable maps on generalized matrix algebras
FEI Xiuhai1, DAI Lei2, ZHU Guowei1
1.School of Mathematics and Physics, Dianxi Science and Technology Normal University, Lincang 677099, Yunnan Province, China
2.School of Mathematics and Statistic, Weinan Normal University, Weinan 714099, Shaanxi Province, China
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摘要： 设$G$是一个2-无挠的广义矩阵代数, $Ω=\{T∈G: T^{2}=0\}$，且$?$是$G$上的一个映射(无可加性假设)。证明了：若对任意的$X,Y,Z∈G且$XYZ∈Ω$,有$?(XYZ)=?(X)YZ+X?(Y)Z+XY?(Z)$，则$?$是一个导子。作为结论的应用,在三角代数、含有单位元和非平凡幂等元的素环、标准算子代数及因子 von Neumann 代数上得到了相同的结论。
关键词： 广义矩阵代数;  导子;  三重可导映射    
Abstract: Let $G$ be a 2-torsion free generalized matrix algebra, $Ω=\{T∈G: T^{2}=0\}$ and $?$ be a mapping from $G$ into itself (without assumption of additivity). In this paper, it is shown that if a map $?$ satisfies $?(XYZ)=?(X)YZ+X?(Y)Z+XY?(Z)$ for all $X,Y,Z∈G$ with $XYZ∈Ω$, then $?$ is a derivation. As its applications, we arrive at similar conclusion on triangular algebras, unital prime rings with a nontrivial idempotent, unital standard operator algebras and factor von Neumann algebras.
Key words: generalized matrix algebra    derivation    triple derivable map
收稿日期: 2019-01-17 出版日期: 2020-03-25
CLC:  O177.1  
基金资助: 国家自然科学基金资助项目(11471199,11501419）；渭南师范学院特色学科建设项目(18TSXK03)；云南省教育厅基础研究基金项目（2020J0748）.
作者简介: 费秀海(1980—)，ORCID:http://orcid.org/ 0000-0002-0772-8964，男，博士，副教授，主要从事算子代数与算子理论研究.
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引用本文:

费秀海, 戴磊, 朱国卫. 广义矩阵代数上的一类局部非线性三重可导映射[J]. 浙江大学学报（理学版）, 2020, 47(2): 167-171.

FEI Xiuhai, DAI Lei, ZHU Guowei. A class of local nonlinear triple derivable maps on generalized matrix algebras. Journal of Zhejiang University (Science Edition), 2020, 47(2): 167-171.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.02.006    或    https://www.zjujournals.com/sci/CN/Y2020/V47/I2/167

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