Skewaffine spaces in the language of distance spaces Original Research Article

In the past André generalized the affine spaces under different aspects to the so-called noncommutative geometries. One of the most general definitions which was inspired by Pfalzgraf (J. Geom. 25 (1985) 147) is that of skewaffine spaces (Ann. Univ. Saraviensis. Ser. Math. 4 (1993) 93). Many interesting results are found but this subject is not much familiar to the geometry community. Maybe the reason for this lies in the language of the axioms used. Here, we will give descriptions of such spaces in the language of distance spaces as proposed by Benz (Geometrische Transformationen, BI-Wissenschaftsverlag, Mannheim, 1992). Moreover, we can find connections to other geometries like Ferrero geometries.