Spread construction of affine partial linear spaces
Affine partial linear spaces (APLSs) were introduced by \textit{K. Radziszewski} [J. Geom. 71, 144-156 (2001; Zbl 1010.51003)]. They are partial linear spaces equipped with a parallelity satisfying Euclid's postulate as well as some basic properties of affine spaces. In the present paper, the author presents algebraic conditions on a pair \((V, {\mathcal G})\), where \(V\) is a vector space and \({\mathcal G}\) a distinguished family of vector subspaces of \(V\), which are equivalent to some axioms arising naturally in the context of APLSs. The independence of some of the axioms is also proved.
scientific article; zbMATH DE number 1760634