Monatshefte für Mathematik

, 149:91 | Cite as

On Maps Preserving Zero Jordan Products

  • Mikhail A. Chebotar
  • Wen-Fong Ke
  • Pjek-Hwee Lee
  • Ruibin Zhang
Article

Abstract.

Let R be a ring, A = Mn(R) and θ: AA a surjective additive map preserving zero Jordan products, i.e. if x,yA are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains \(\frac{1}{2}\) and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: AA is a Jordan homomorphism.

2000 Mathematics Subject Classification: 15A04, 47B49 
Key words: Map preserving zero Jordan products, Jordan homomorphism, functional identity, d-free subset 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Mikhail A. Chebotar
    • 1
  • Wen-Fong Ke
    • 2
  • Pjek-Hwee Lee
    • 3
  • Ruibin Zhang
    • 4
  1. 1.Southern Taiwan University of TechnologyYung-KangTaiwan
  2. 2.National Cheng Kung UniversityTainanTaiwan
  3. 3.National Taiwan UniversityTaipeiTaiwan
  4. 4.University of SydneyAustralia

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