Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 2010 - Volume 140, Issue 01  

Research Article

Matrix maps over planar near-rings

Wen-Fong Kea1, Johan H. Meyera2 and Gerhard Wendta3

a1 Department of Mathematics, National Cheng Kung University, and National Center for Theoretical Sciences (South), Taiwan 701, Taiwan, (wfke@math.ncku.edu.tw)

a2 Department of Mathematics and Applied Mathematics, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa, (meyerjh.sci@ufs.ac.za)

a3 Department of Algebra, Johannes Kepler Universität Linz, Altenberger Strasse 69, 4040 Linz, Austria, (wendt@algebra.uni-linz.ac.at)

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.

(Received October 06 2008)

(Accepted May 15 2009)

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