Algebraic properties of some configurational propositions
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.
scientific article; zbMATH DE number 1053889