Vukman, Joso An identity related to centralizers in semiprime rings. (English) Zbl 1014.16021 Commentat. Math. Univ. Carol. 40, No. 3, 447-456 (1999). Let \(R\) be an associative ring. Recall that an additive mapping \(T\colon R\to R\) is called a left (right) centralizer if \(T(xy)=T(x)y\) (\(T(xy)=xT(y)\)) for all \(x,y\in R\). The author proves that if \(R\) is a \(2\)-torsionfree semiprime ring and \(T\colon R\to R\) is an additive mapping such that \(2T(x^2)=T(x)x+xT(x)\) for each \(x\in R\), then \(T\) is a left and right centralizer. Reviewer: Ladislav Bican (Praha) Cited in 30 Documents MSC: 16N60 Prime and semiprime associative rings 16R50 Other kinds of identities (generalized polynomial, rational, involution) 16W20 Automorphisms and endomorphisms 16W10 Rings with involution; Lie, Jordan and other nonassociative structures Keywords:prime rings; semiprime rings; Jordan derivations; right centralizers; left Jordan centralizers PDFBibTeX XMLCite \textit{J. Vukman}, Commentat. Math. Univ. Carol. 40, No. 3, 447--456 (1999; Zbl 1014.16021) Full Text: EuDML