Regular spreads and chain geometries (Q1971027)

A translation plane \({\mathcal A}\) can be constructed from a spread \(S\) of a projective space over a not necessarily commutative field \(K\). In [\textit{T. Grundhöfer}, Geom. Dedicata 11, 227-237 (1981; Zbl 0492.51003)], it was proved that (if \(|K|> 2\)) \(S\) is regular if and only if \({\mathcal A}\) is a Moufang plane and \(K\) is contained in the center of its coordinate alternative field. The author gives a new proof of this theorem by means of chain geometries (= certain incidence structures constructed from associative algebras).