理论数学  >> Vol. 6 No. 3 (May 2016)

域上矩阵保乘积的诱导映射
Induced Maps Preserving Multiplicative Matrices over Fields

DOI: 10.12677/PM.2016.63025, PDF, HTML, XML, 下载: 1,206  浏览: 2,927 

作者: 张 隽*, 曹重光:黑龙江大学,黑龙江 哈尔滨

关键词: 保乘积诱导映射Field Preserving Multiplicative Induced Map

摘要:

令F是一个域,Sn(F)是F上所有n*n对称矩阵的集合。如果一个映射f:Sn(F)→Sn(F)被定义如下,∫:B=(bij)|→(fij(bij)), ∀B∈Sn(F)

其中,{fij|i≤j∈{1,2,...,n}}是关于F的函数集,则称f是Sn(F)的由{fij}诱导的映射。如果对于A,B∈Sn(F)有f(AB)=f(A)f(B),则f被称为保矩阵乘积。本文我们刻画域上矩阵保乘积的诱导映射。

Abstract: Let F be a field, Sn(F) be the set of all n*n matrices over F. If a map f:Sn(F)→Sn(F) is defined by ∫:B=(bij)|→(fij(bij)) where {fij|i≤j∈{1,2,...,n}} is the set of functions on F, then f is called a map induced by {fij} on Sn(F). If A,B∈Sn(F) implies f(AB)=f(A)f(B), then f is called preserving multiplicative matrices. In this paper, we characterize induced maps preserving multiplicative matrices over fields.

文章引用: 张隽, 曹重光. 域上矩阵保乘积的诱导映射[J]. 理论数学, 2016, 6(3): 166-171. http://dx.doi.org/10.12677/PM.2016.63025

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