A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Lie maps on alternative rings preserving idempotents

Volume 166 / 2021

Bruno Leonardo Macedo Ferreira, Henrique Guzzo Jr., Ivan Kaygorodov Colloquium Mathematicum 166 (2021), 227-238 MSC: Primary 17A36; Secondary 17D05. DOI: 10.4064/cm8195-10-2020 Published online: 1 April 2021

Abstract

Let $\mathfrak R$ and $\mathfrak R’$ be unital $2$,$3$-torsion free alternative rings and $\varphi : \mathfrak R \rightarrow \mathfrak R’$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\mathfrak R$ has a nontrivial idempotent. Under certain assumptions on $\mathfrak R$, we prove that $\varphi $ is of the form $\psi + \tau $, where $\psi $ is either an isomorphism or the negative of an anti-isomorphism of $\mathfrak R$ onto $\mathfrak R’$ and $\tau $ is an additive mapping of $\mathfrak R$ into the centre of $\mathfrak R’$ which maps commutators to zero.

Authors

  • Bruno Leonardo Macedo FerreiraFederal University of Technology
    Professora Laura Pacheco Bastos Avenue, 800
    85053-510, Guarapuava, Brazil
    e-mail
  • Henrique Guzzo Jr.Institute of Mathematics
    University of São Paulo
    Matão Street, 1010
    05508-090, São Paulo, Brazil
    e-mail
  • Ivan KaygorodovFederal University of ABC
    dos Estados Avenue, 5001
    09210-580, Santo André, Brazil
    and
    Moscow Center for Fundamental and Applied Mathematics
    Moscow, 119991, Russia
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image