Glasnik Matematicki, Vol. 38, No.2 (2003), 253-261.

AN EQUATION RELATED TO CENTRALIZERS IN SEMIPRIME RINGS

Joso Vukman and Irena Kosi-Ulbl

Department of Mathematics, University of Maribor, PEF, Koroška 160, 2000 Maribor, Slovenia
e-mail: joso.vukman@uni-mb.si
e-mail: irena.kosi@uni-mb.si


Abstract.   Let R be a 2-torsion free semiprime ring with extended centroid C and let T : R R be an additive mapping. Suppose that 3T(xyx) = T(x)yx + xT(y)x + xyT(x) holds for all x,y R. Then there exists an element λ C such that T(x) = λ x for all x R.

2000 Mathematics Subject Classification.   16N60, 39B05.

Key words and phrases.   Prime ring, semiprime ring, derivation, Jordan derivation, Jordan triple derivation, left (right) centralizer, left (right) Jordan centralizer, centralizer.


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