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On certain equations in rings

Published online by Cambridge University Press:  17 April 2009

Joso Vukman
Affiliation:
Department of Mathematics, University of Maribor, PeF, Koroska 160, SI-2000 Maribor, Slovenia, e-mail: [email protected], [email protected], [email protected]
Irena Kosi-Ulbl
Affiliation:
Department of Mathematics, University of Maribor, PeF, Koroska 160, SI-2000 Maribor, Slovenia, e-mail: [email protected], [email protected], [email protected]
Daniel Eremita
Affiliation:
Department of Mathematics, University of Maribor, PeF, Koroska 160, SI-2000 Maribor, Slovenia, e-mail: [email protected], [email protected], [email protected]
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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: RR such that T(xyx) = T(x)yxxT(y)x + xyT(x) holds for all pairs x, yR. 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
Copyright
Copyright © Australian Mathematical Society 2005

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