Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-09T09:15:41.878Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)