AN IDENTITY RELATED TO θ-CENTRALIZERS IN SEMIPRIME RINGS

Document Type : Original Manuscript

Author

Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.

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 $θ(Z(R))=Z(R)$.

Keywords

References

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Journal of Algebraic Systems
Volume 12, Issue 2
January 2025
Pages 367-377

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