Abstract
In Karzel et al. (J. Geom. 99: 116–127, 2009) we introduced for a symmetric Minkowski plane \({ {\mathfrak M} := (P,\Lambda,{\mathfrak G}_1,{\mathfrak G}_2) }\) an order concept by the notion of an orthogonal valuation for the circles of Λ and showed that there is a one to one correspondence between the valuations and the halforderings of the accompanying commutative field. Here we consider an order concept which is based on the notion of separation for quadruples of concyclic points and establish the connections between these two notions. Our main result (cf. Theorem 3.3) states that these concepts are equivalent.
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Karzel H., Kosiorek J., Matraś A.: Ordered symmetric Minkowski planes I. J. Geom. 93, 116–127 (2009)
Kroll H.-J.: Anordnungsfragen in Benz-Ebenen. Abh. Math. Semin. Univ. Hambg. 46, 217–255 (1977)
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Dedicated to Mario Marchi
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Karzel, H., Kosiorek, J. & Matraś, A. Symmetric Minkowski planes ordered by separation. J. Geom. 98, 115–125 (2010). https://doi.org/10.1007/s00022-010-0045-z
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DOI: https://doi.org/10.1007/s00022-010-0045-z