Hyperaffine planes over hyperfields (Q1904263)

The authors first study hyperaffine planes coordinatized over planar hyperfields. The main purpose of the paper is to show that if an abstract hyperaffine plane satisfies certain additional conditions 1-11, then there exists a hyperfield such that the coordinate plane over this hyperfield is isomorphic to the given hyperaffine plane. It seems that the extra conditions 1-11 are not necessarily true in every hyperaffine plane over a planar hyperfield. This point is not discussed in the paper. The methods are similar, though more involved, to the standard coordinatization of translation planes.