数学

一类代数上的弱可加交换映射

  • 霍东华
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  • 1. 牡丹江师范学院 数学科学学院, 黑龙江 牡丹江 157012;
    2. 哈尔滨工业大学 数学学院, 哈尔滨 150001
霍东华,女,博士,副教授,研究方向为代数学.E-mail:i94donghua@163.com.

收稿日期: 2018-07-27

  网络出版日期: 2019-07-18

基金资助

黑龙江省省属高等学校基本科研业务费重点项目(1354ZD007);牡丹江师范学院博士科研启动基金(MNUB201512)

Characterization of commuting weakly additive maps on a class of algebras

  • HUO Dong-hua
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  • 1. School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang Heilongjiang 157012, China;
    2. School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received date: 2018-07-27

  Online published: 2019-07-18

摘要

A是一个有单位元1的代数.称映射fAA是一个弱可加映射,如果满足对任意的x,yA,存在tx,ysx,y∈F使得fx+y)=tx,yfx)+sx,yfy)成立.本文证明了在一定的假设下,如果f是交换映射,则存在λ0x) ∈A和一个从AZA)的映射λ1,使得对所有的xAfx)=λ0xx1x).作为应用,刻画了Mn(F)上一类交换的弱可加映射.

本文引用格式

霍东华 . 一类代数上的弱可加交换映射[J]. 华东师范大学学报(自然科学版), 2019 , 2019(4) : 1 -10,18 . DOI: 10.3969/j.issn.1000-5641.2019.04.001

Abstract

Let A be an algebra with unit 1. A map f:AA is a weakly additive map if for every x, yA there exist tx,y, sx,y∈F such that f(x + y)=tx,yf(x) + sx,yf(y). We prove that under some conditions, if f is a commuting map, then there exists λ0(x)∈A and a map λ1 from A into Z(A) such that f(x)=λ0(x)x + λ1(x) for all xA. As an application, a class of commuting weakly additive maps on Mn(F) are characterized.

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