Algebraic properties of some configurational propositions
type: Item
instance of: scholarly article
title: Algebraic properties of some configurational propositions
zbMATH Open document ID: 0881.51004
DOI: 10.1007/BF01229565
author: Khuloud Ghalieh
published in: Journal of Geometry
publication date: 1998-01-22T00:00:00Z
review text: In projective planes the Desargues and the Pappus configurations have many degenerate forms. The author investigates several such forms as well as the axiom \(F\) which requires that the diagonal points of every complete quadrangle are collinear. Many of these configurations turn out to be equivalent. An algebraic formulation of axiom \(F\) is given, namely if \(a \cdot b = c\) for \(a,b,c\) with \(c \neq 0\) of any coordinatizing ternary ring \((T,\tau)\), then \(\tau(a,b,c)=0\). The latter condition is equivalent to \(1+1=0\). Similar algebraic conditions are derived for the other configurations.
Mathematics Subject Classification ID: 51A20
zbMATH DE Number: 1053889
zbMATH Keywords: Desargues configuration
zbMATH Keywords: Pappus configuration
zbMATH Keywords: ternary ring
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1053889