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Finiteness Conditions for Near-Rings

Published online by Cambridge University Press:  20 November 2018

H. E. Heatherly  and
J. D. P. Meldrum
H. E. Heatherly
Affiliation:
Department of Mathematics University of Southwestern Louisiana Layfayette, Louisiana 70504 U.S.A.
J. D. P. Meldrum
Affiliation:
Department of Mathematics King's Buildings University of Edinburgh Edinburgh EH9 3JZ Scotland
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Abstract

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There have been a number of papers which give necessary conditions for a ring to be finite, and a few, most notably H. E. Bell [1], which do the same for near-rings. We wish to make a contribution to this latter theme. Most of Bell's results concern distributive near-rings. Our main contribution is to extend a number of these results to weakly distributive near-rings.

Keywords

16A76
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 492 - 496
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bell, H. E., Onfiniteness of near-rings, Publ. Math. Debrecen 31(1984), 77–80.Google Scholar
2. Lyons, C. G. and J. Meldrum, D. P., Reduction theorems for endomorphism near-rings, Monats. Math. 89(1980), 301–313.Google Scholar
3. Meldrum, J. D. P., Near-rings and their links with groups, Research Notes 134, Pitman (London), 1985.Google Scholar
4. Pilz, G., Near-rings, Revised Edition, North-Holland (Amsterdam), 1987.Google Scholar
5. Szele, T., On afiniteness criterion for modules, Publ. Math. Debrecen 3(1954), 253–256.Google Scholar