Proves that a specific additive mapping is a θ-centralizer in semiprime rings, indicating structural properties.
Let R be a $ 2$-torsion-free semiprime ring and θ be an epimorphism of R. In this paper, under special hypotheses, we prove that if T: R R is an additive mapping such that$$T(xyx)=θ(x)T(y)θ(x),$$holds for all x, y∈ R, then T is a $θ$-centralizereither R is unital or $θ(Z(R))=Z(R)$.
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Abbas Zivari-Kazempour (2023) studied this question.
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