AN IDENTITY RELATED TO θ-CENTRALIZERS IN SEMIPRIME RINGS | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 2، فروردین 2025، صفحه 367-377 اصل مقاله (124.89 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.11856.1607 | ||
| نویسنده | ||
| Abbas Zivari-Kazempour* | ||
| Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran. | ||
| چکیده | ||
| 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 $θ(Z(R))=Z(R)$. | ||
| کلیدواژهها | ||
| semiprime ring؛ centralizer؛ $\theta$-centralizer؛ epimorphism | ||
| مراجع | ||
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