保域上矩阵可交换{1}-逆的线性映射  

Linear Maps Preserving Commutative {1}-Inverses of Matrices over Fields

作　　者：周洪玲[1] 范广慧[1] 苏在滨[1] 卜长江[2] ZHOU Hong-ling;FAN Guang-hui;SU Zai-bin;BU Chang-jiang(Department of Mathematics,Heilongjiang Engineering College,Harbin 150050,China;College of Science,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]黑龙江工程学院数学系,黑龙江哈尔滨150050 [2]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨理工大学学报》2010年第2期67-70,共4页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅科学技术研究项目(11521240)

摘　　要：设F是一个特征不为2且至少含有5个元素的域.令Mn(F)为F上的n×n全矩阵代数.刻画了Mn(F)上保持矩阵可交换{1}-逆的线性映射的形式.利用保幂等结论证明了f为Mn(F)上的保持矩阵可交换{1}-逆的非零线性映射,当且仅当存在P∈GLn(F),使得f(A)=εPAP^(-1),A∈Mn(F),ε=±1∈F;或者存在P∈GL_(n)(F),使得f(A)=εPAtP^(-1),A∈Mn(F),ε=±1∈F.Suppose F is a field of characteristic not 2 with at least five elements.Let Mn(F)be the n×n full matrix algebra over F.The forms of linear maps preserving commutative{1}-inverses of matrices over Mn(F)are characterized.Using the conclusions of idempotent-preserving,it is proved that f is the nonzero linear maps from Mn(F)to Mn(F)preserving commutative{1}-inverses of matrices,if and only if there exists P∈GLn(F),such that f(A)=εPAP^(-1),A∈Mn(F),ε=±1∈F,or there exists P∈GL_(n)(F),such that f(A)=εPAtP^(-1),A∈Mn(F),ε=±1∈F.

关 键 词：域 线性映射 可交换{1}-逆 

分 类 号：O151.21[理学—数学]