Anordnung in Rechtseitebenen und Integritätssystemen

H. Karzel [6] has shown that rectangular planes can be algebraically represented by metric integral systems. Here, rectangular planes, which are simultaneously ordered planes, are considered. Necessary and sufficient conditions on the integral system are given for the corresponding rectangular plane to be ordered.Moreover, it is shown that the maximal multiplicative system of an ordered rectangular plane is a valuation ring.