Projective Klingenberg planes over nearrings (Q1207029)

A projective Klingenberg plane is an incidence structure with equivalence relation on the set of points resp. of lines such that there is an incidence epimorphism onto a projective plane. It is shown that examples of such planes can be given by a sort of local nearrings which are therefore called PK-nearrings. The connection with the already known coordinatization by local ternary rings is pointed out [\textit{D. Keppens}, Simon Stevin 62, No. 1, 63-90 (1988; Zbl 0652.51004)]. Examples of PK- nearrings are given with the help of formal power series, in which the multiplication is twisted by a coupling.