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Centralisers on rings and algebras

Published online by Cambridge University Press:  17 April 2009

Joso Vukman  and
Irena Kosi-Ulbl
Joso Vukman
Affiliation:
Department of Mathematics, University of Maribor, PEF, Koroška 160, 2000 Maribor, Slovenia, e-mail: joso.vukman@uni-mb.si, irena.kosi@uni-mb.si
Irena Kosi-Ulbl
Affiliation:
Department of Mathematics, University of Maribor, PEF, Koroška 160, 2000 Maribor, Slovenia, e-mail: joso.vukman@uni-mb.si, irena.kosi@uni-mb.si
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In this paper we investigate identities related to centralisers in rings and algebras. We prove, for example, the following result. Let A be a semisimple H* -algebra and let T: A → A be an additive mapping satisfying the relation T(xm+n+1) = xmT(x)xn for all x ∈ A and some integers m ≥ 1, n ≥ 1. In this case T is a left and a right centraliser.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 225 - 234
Copyright
Copyright © Australian Mathematical Society 2005

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