AN IDENTITY RELATED TO θ-CENTRALIZERS IN SEMIPRIME RINGS

Author(s):

Abbas Zivari-Kazempour *

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

‎Let $R$ be a $ 2$-torsion-free semiprime ring and $\theta$ be an epimorphism of $R$‎. ‎In this paper‎, ‎under special hypotheses‎, we prove that if $T‎: ‎R\longrightarrow R$‎ ‎is an additive mapping such that‎‎$‎‎$‎‎T(xyx)=θ(x)T(y)θ(x)‎,‎$‎‎$‎‎holds for all $x‎, ‎y\in R$‎, ‎then‎ ‎$T$ is a $θ$-centralizer‎either $R$ is unital‎ or $θ(Z(R))=Z(R)$.

Keywords:

semiprime ring‎ , ‎centralizer‎ , ‎$ , theta$-centralizer‎ , ‎epimorphism

Language:
English
Published:
Journal of Algebraic Systems, Volume:12 Issue: 2, Winter-Spring 2025
Pages:
367 to 377
https://www.magiran.com/p2637390