A NEW GENERALIZATION OF MOULTON AFFINE PLANES

We consider a variation on W. A. Pierce's construction of Moulton planes. For any pseudo-ordered field F, the pairs of elements of F are taken as points, and straight lines are given by the equations x = c, y = mx + n with m greater-than-or-equal-to 0 and g(y) = mf(x)+n with m < 0, where f and g are mappings of F into itself which have to satisfy a number of conditions.