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Boolean Near-Rings

Published online by Cambridge University Press:  20 November 2018

James R. Clay  and
Donald A. Lawver
James R. Clay
Affiliation:
University of Arizona, Tucson, Arizona 85721
Donald A. Lawver
Affiliation:
University of Arizona, Tucson, Arizona 85721
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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].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 3 , June 1969 , pp. 265 - 273
Copyright
Copyright © Canadian Mathematical Society 1969

References

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