Semiorderings and localizations of planar ternary rings

We continue our study of quadratic semiorderings in planar ternary rings started in [11]. Following PRESTEL [16] and LAM [14], we establish the notion of compatibility between semiorderings and places of planar ternary rings and transfer a Baer-Krull like theorem for semiorderings to our setting. As in the classic case, any archimedean semiordering turns out to be an ordering. Finally, we show that over planar ternary rings with rational prime field each semiordering gives rise to a natural place into the reals.