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Matrix maps over planar near-rings

Published online by Cambridge University Press:  04 February 2010

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

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 83 - 99
Copyright
Copyright © Royal Society of Edinburgh 2010

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