Journal of East China Normal University(Natural Sc ›› 2019, Vol. 2019 ›› Issue (4): 1-10,18.doi: 10.3969/j.issn.1000-5641.2019.04.001

• Mathematics •     Next Articles

Characterization of commuting weakly additive maps on a class of algebras

HUO Dong-hua1,2   

  1. 1. School of Mathematical Sciences, Mudanjiang Normal University, Mudanjiang Heilongjiang 157012, China;
    2. School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
  • Received:2018-07-27 Online:2019-07-25 Published:2019-07-18

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.

Key words: algebras, commuting maps, weakly additive maps

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