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Near-rings of mappings*

Published online by Cambridge University Press:  14 November 2011

J. D. P. Meldrum  and
A. Oswald
J. D. P. Meldrum
Affiliation:
Department of Mathematics, University of Edinburgh
A. Oswald
Affiliation:
Department of Mathematics and Statistics, Teesside Polytechnic, Middlesbrough
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Synopsis

This paper is concerned with the structure of M = Maps(G), the near-ring of all mappings from a group G to itself which commute with a group S* of automorphisms of G. Here S is S* together with the zero endomorphism. Necessary and sufficient conditions on the pair (G, S) are obtained for M to be (i) regular, (ii) unit regular, (iii) an equivalence near-ring. These conditions take a very simple form. In the case (iii), the two-sided M-subgroups of M are determined. The next result shows that under suitable conditions, M is a simple near-ring. A definition of transitivity is given for subnear-rings of M, and some properties of transitive near-rings are proved. Finally two examples are given to show that all the classes of near-rings considered are distinct.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 213 - 223
Copyright
Copyright © Royal Society of Edinburgh 1979

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