In this paper we shall establish the notion of compatibility between preorderings and places for planar ternary rings. The theorem of Baer and Krull concerning the relationship between the orderings of a field K, compatible with a place n:K--* K'w {oo}, and the space of orderings of K' is extended to ternary rings. We study the notion of fans and SAP-preorderings over ternary rings and prove that no Archimedean ordering contains a non-trivial fan. Finally the local stability formula of BrScker is carried over to ternary rings. EINLEITUNGGeometriae Dedicata 27 (1988), 137-151.

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We introduce a new notion of valuations on planar ternary rings (PTRs), which allows us to extend some results concerning the relations between orderings and valuations of fields to PTRs. Our concept generalizes van Maldeghem's notion of PTRs with valuation, coordinatizing the buildings at infinity of discrete triangle buildings.