形式矩阵环上的σ-双导子和σ-交换映射  

σ-biderivations and σ-commuting Mappings of Formal Matrix Rings

作　　者：李玉 唐高华 LI Yu;TANG Gaohua(School of Mathematics and Statistics,Southwest University,Chongqing,400715,P.R.China;College of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi,541004,P.R.China;School of Sciences,Beibu Gulf University,Qinzhou,Guangxi,535011,P.R.China)

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]广西师范大学数学与统计学院,桂林广西541004 [3]北部湾大学理学院,钦州广西535011

出　　处：《数学进展》2021年第2期195-213,共19页Advances in Mathematics（China）

基　　金：Supported by NSFC (Nos.11661014,11661013,11961050);Guangxi Natural Science Foundation (No.2016GXSFDA380017)。

摘　　要：令(R N M S)是一个具有零迹理想的形式矩阵环,σ是K的一个满足σ(E_(11))=E_(11),σ(E_(22))=E_(22)的自同构.本文确定了K的σ-双导子和σ-交换映射的一般形式,证明了在一定条件下K的每个σ-双导子都可以表示成一个外σ-双导子与一个内σ-双导子的和.此外,本文给出了K的任意σ-双导子(σ-交换映射)是内σ-双导子(真σ-交换映射)的一个充分条件.Let (R N M S) be a formal matrix ring with zero trace ideals and σ an automorphism of K with σ(E_(11))=E_(11) and σ(E_(22))=E_(22).In this paper,we determine the general form of σ-biderivations and σ-commuting mappings of K,and prove that under certain conditions every σ-biderivation of K is a sum of an inner σ-biderivation and an extremalσ-biderivation.Moreover,we give a sufficient condition on K for all of its σ-biderivations(respectively,σ-commuting mappings) to be inner(respectively,proper).

关 键 词：形式矩阵环 σ-导子 σ-双导子 σ-交换映射 

分 类 号：O153.3[理学—数学]