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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