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三角代数上的一类非线性可交换映射 被引量：2

A Class of Nonlinear Commuting Maps on Triangular Algebras
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摘要 运用矩阵分块方法研究三角代数上的一类非线性可交换映射:模线性可交换映射.刻画了此类映射的具体形式,给出了三角代数上模线性可交换映射是真可交换映射的充分条件,并证明了套代数上的每个模线性可交换映射都是真可交换映射. The authors studied a class of nonlinear commuting maps （namely, modulo linear commuting map）on triangular algebras,described the forms of such maps,and gave such a sufficient condition that every modulo linear commuting map on triangular algebras is proper. As an application,it is proved that every modulo linear commuting map on nest algebras is proper.
作者 余维燕 张建华
机构地区 海南师范大学数学与统计学院 陕西师范大学数学与信息科学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2014年第5期881-887,共7页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10971123) 教育部博士学科点重点建设项目(批准号:20110202110002) 海南省自然科学研究计划项目(批准号:113004 113007) 海南省教育厅高校科研重点项目(批准号:HNKY2014-34)
关键词 三角代数 可交换映射 模线性映射 triangular algebra commuting map modulo linear map
分类号 O177.1 [理学—基础数学]
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参考文献19

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二级参考文献12

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共引文献2

同被引文献7

  • 1BRESAR M. On generalized biderivations and related maps[Jl. Algebra, 1995, 172(3) : 764 -786.
  • 2DOMINIK B. Biderivations of triangular algebras [ J ]. Linear Algebra and Its Applications, 2009, 431 ( 9 ) : 1587 - 1602.
  • 3ZHANG J H, FENG S, LI H X, et al. Generalized bi- derivations of nest algebras [ J ]. Linear Algebra and Its Applications, 2006, 418( 1): 225-233.
  • 4MOHAMMAD A. On generalized (o',r)-biderivations in rings [ J ]. Asian-European Journal of mathematics, 2011, 4(3) : 389 -402:.
  • 5REHMAN N. On Lie ideals and generalized Jordan left derivations of prime rings [ J ]. Ukrainian Mathematics Journal, 2014, 65(8): 1118-1125.
  • 6CHEUNG W S. Commuting maps of triangular algebras I J]. Journal of the London Mathematical Society, 2001, 63(1) : 117.
  • 7刘莉君.Banach代数上的高阶Jordan-triple导子系的广义Hyers-Ulam-Rassias稳定性[J].纯粹数学与应用数学,2011,27(5):642-649. 被引量：2

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吉林大学学报（理学版）
2014年 第5期

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