Journal of East China Normal University(Natural Science) >

2019 , Vol. 2019 >Issue 4: 1 - 10,18

DOI: https://doi.org/10.3969/j.issn.1000-5641.2019.04.001

Mathematics

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

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Abstract

Let A be an algebra with unit 1. A map f:A→A is a weakly additive map if for every x, y∈A 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 x∈A. As an application, a class of commuting weakly additive maps on Mn(F) are characterized.

Key words： algebras; commuting maps; weakly additive maps

Cite this article

HUO Dong-hua . Characterization of commuting weakly additive maps on a class of algebras[J]. Journal of East China Normal University(Natural Science), 2019 , 2019(4) : 1 -10,18 . DOI: 10.3969/j.issn.1000-5641.2019.04.001

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