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arXiv · 1905.03859

Ordered Line and Skew-Fields in the Desargues Affine Plane

Orgest Zaka·James F. Peters
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Abstract

This paper introduces ordered skew fields that result from the construction of a skew field over an ordered line in a Desargues affine plane. A special case of a finite ordered skew field in the construction of a skew field over an ordered line in a Desargues affine plane in Euclidean space, is also considered. Two main results are given in this paper: (1) every skew field constructed over a skew field over an ordered line in a Desargues affine plane is an ordered skew field and (2) every finite skew field constructed over a skew field over an ordered line in a Desargues affine plane in $\mathbb{R}^2$ is a finite ordered skew field.

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Orgest Zaka, James F. Peters. 2019-05-08. Ordered Line and Skew-Fields in the Desargues Affine Plane. https://arxiv.org/abs/1905.03859

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