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Matrix maps over planar near-rings

Published online by Cambridge University Press:  04 February 2010

Wen-Fong Ke
Department of Mathematics, National Cheng Kung University, and National Center for Theoretical Sciences (South), Taiwan 701, Taiwan, (
Johan H. Meyer
Department of Mathematics and Applied Mathematics, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa, (
Gerhard Wendt
Department of Algebra, Johannes Kepler Universität Linz, Altenberger Strasse 69, 4040 Linz, Austria, (


Following a method by Meldrum and van der Walt, near-rings of matrix maps are defined for general near-rings, not necessarily with identity. The influence of one-sided identities is discussed. When the base near-ring is integral and planar, the near-ring of matrix maps is shown to be simple. Various types of primitivity of the near-ring of matrix maps are discussed when the base near-ring is planar but not integral. Finally, an open problem concerning bijective matrix maps is solved.

Research Article
Copyright © Royal Society of Edinburgh 2010

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