Ordered Line and Skew-Fields in the Desargues Affine Plane

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.

14 pages, 9 figures

References in corpus (2)

• The Transform of a line of Desargues Affine Plane in an additive Group of its Points
• Isomorphic-Dilations of the skew-fields constructed over parallel lines in the Desargues affine plane

Cited by in corpus (4)

• The Endomorphisms Algebra of Translations Group and Associative Unitary Ring of Trace-Preserving Endomorphisms in Affine Plane
• Skew-Field of Trace-Preserving Endomorphisms, of Translation Group in Affine Plane
• Laplace Method for calculate the Determinant of cubic-matrix of order 2 and order 3
• The Determinant of Cubic-Matrix of order 2 and order 3: Some basic Properties and Algorithms