An identity related to \(\theta\)-centralizers in semiprime rings. (English) Zbl 1531.16014
Summary: 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 \(T(xyx)=\theta(x)T(y)\theta(x)\) holds for all \(x, y\in R\), then \(T\) is a \(\theta\)-centralizer.
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