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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (12): 42-47.doi: 10.6040/j.issn.1671-9352.0.2017.255

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三角代数上Lie积为平方零元的非线性Jordan可导映射

武鹂,张建华*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2017-05-22 出版日期:2017-12-20 发布日期:2017-12-22
  • 通讯作者: 张建华(1965— ), 男, 博士,教授,博士生导师, 研究方向为算子代数. E-mail:jhzhang@snnu.edu.cn E-mail:wuli@snnu.edu.cn
  • 作者简介:武鹂(1991— ), 女, 硕士研究生, 研究方向为算子代数. E-mail:wuli@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11471199)

Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements

WU Li, ZHANG Jian-hua*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Received:2017-05-22 Online:2017-12-20 Published:2017-12-22

摘要: 设U=Tri(A, M, B )是特征不为 2 的三角代数, Q={u∈U:u2=0}且φ:U→U是一个映射(无可加或线性假设)。 证明了如果对任意a,b∈U且[a,b]∈Q, 有φ(ab)=φ(a)b+aφ(b), 则φ是一个可加导子, 其中[a,b]=ab-ba为Lie积, ab=ab+ba为Jordan积。

关键词: 三角代数, 平方零元, Jordan可导映射

Abstract: Let U=Tri(A, M, B )be a 2-torsion free triangular algebra, and Q={u∈U:u2=0}. We prove that if a map φ:U→U satisfies φ(ab)=φ(a)b+aφ(b)for any a,b∈U with [a,b]∈Q, then φ is an additive derivation, where [a,b]=ab-ba is the Lie product and ab=ab+ba is the Jordan product.

Key words: square zero element, triangular algebra, Jordan derivable map

中图分类号: 

  • O177.1
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[1] 胡丽霞,张建华. 三角代数上的零点Lie高阶可导映射[J]. J4, 2013, 48(4): 5-9.
[2] 曹宗霞,张建华. 一类环上的Jordan可导映射[J]. J4, 2012, 47(4): 5-10.
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