Author:
Clay James R.,Lawver Donald A.
Abstract
In this paper we introduce the concept of Boolean near-rings. Using any Boolean ring with identity, we construct a class of Boolean near-rings, called special, and determine left ideals, ideals, factor near-rings which are Boolean rings, isomorphism classes, and ideals which are near-ring direct summands for these special Boolean near-rings.Blackett [6] discusses the near-ring of affine transformations on a vector space where the near-ring has a unique maximal ideal. Gonshor [10] defines abstract affine near-rings and completely determines the lattice of ideals for these near-rings. The near-ring of differentiable transformations is seen to be simple in [7], For near-rings with geometric interpretations, see [1] or [2].
Publisher
Canadian Mathematical Society
Cited by
6 articles.
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1. BZS Near-Rings and Rings;Springer Proceedings in Mathematics & Statistics;2021
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4. Concerning nil groups for near-rings;Acta Mathematica Academiae Scientiarum Hungaricae;1972-09
5. The structure of a special class of near-rings;Journal of the Australian Mathematical Society;1972-03