caa a22 4500 465825133 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19900401xx s 000 0 eng 10.1007/BF01833146 doi (NATIONALLICENCE)springer-10.1007/BF01833146 Kalhoff Franz Fachbereich Mathematik, Universität Dortmund, Postfach 50 05 00, D-4600, Dortmund 50, West Germany aut Trivialization of fans in planar ternary rings with rational prime field [Elektronische Daten] [Franz Kalhoff] Summary: Making use of the intimate relations between real places and orderings, we continue studying the spaces of orderings of planar ternary rings (PTRs) with rational prime field. As in the classical case, given a preorderingS of such a PTRT, then the productA S of all natural place ringsA p associated to the orderingsP ∈ X/S is itself a place ring ofT. In particular, ifS is a nontrivial fan ofT thenA s ≠ T. Thus L. Bröcker's celebrated theorem on the trivialization of fans also applies to our setting: For any fan Sof a PTRT with rational prime field there exists a place µ: T → T′ ∪ {∞} such that the push down S′:= μ(S)\{0,∞} of S is a trivial fan of T′. Further, Bröcker's global stability formula and, by means of an approximation theorem, some classical, valuation theoretic characterizations of SAP-preorderings and fans also extend to PTRs with rational prime field. Birkhäuser Verlag, 1990 Primary 51G05 nationallicence Secondary 11E81, 12K05, 12K10 nationallicence aequationes mathematicae Birkhäuser-Verlag 39/2-3(1990-04-01), 149-160 0001-9054 39:2-3<149 1990 39 10 https://doi.org/10.1007/BF01833146 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01833146 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kalhoff Franz Fachbereich Mathematik, Universität Dortmund, Postfach 50 05 00, D-4600, Dortmund 50, West Germany aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 39/2-3(1990-04-01), 149-160 0001-9054 39:2-3<149 1990 39 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer