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Information Journal Paper

Title

AN IDENTITY RELATED TO θ-CENTRALIZERS IN SEMIPRIME RINGS

Pages

  367-377

Keywords

‎$\theta$-centralizer‎ 

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 $θ$-centralizer either $R$ is unital or $θ(Z(R))=Z(R)$.

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