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On certain equations in rings

Published online by Cambridge University Press:  17 April 2009

Joso Vukman ,
Irena Kosi-Ulbl  and
Daniel Eremita
Joso Vukman
Affiliation:
Department of Mathematics, University of Maribor, PeF, Koroska 160, SI-2000 Maribor, Slovenia, e-mail: joso.vukman@uni-mb.si, irena.kosi@uni-mb.si, daniel.eremita@uni-mb.si
Irena Kosi-Ulbl
Affiliation:
Department of Mathematics, University of Maribor, PeF, Koroska 160, SI-2000 Maribor, Slovenia, e-mail: joso.vukman@uni-mb.si, irena.kosi@uni-mb.si, daniel.eremita@uni-mb.si
Daniel Eremita
Affiliation:
Department of Mathematics, University of Maribor, PeF, Koroska 160, SI-2000 Maribor, Slovenia, e-mail: joso.vukman@uni-mb.si, irena.kosi@uni-mb.si, daniel.eremita@uni-mb.si
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In this paper we prove the following result: Let R be a 2-torsion free semiprime ring. Suppose there exists an additive mapping T: R → R such that T(xyx) = T(x)yx − xT(y)x + xyT(x) holds for all pairs x, y ∈ R. Then T is of the form 2T(x) = qx + xq, where q is a fixed element in the symmetric Martindale ring of quotients of R.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 53 - 60
Copyright
Copyright © Australian Mathematical Society 2005

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