Cyclic 2-structures and spaces of orderings of power series fields in two variables

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2011
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Marshall, Murray
Osiak, Katarzyna
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Zusammenfassung

We consider the space of orderings of the field R((x,y)) and the space of orderings of the field R((x))(y), where R is a real closed field. We examine the structure of these objects and their relationship to each other. We define a cyclic 2-structure to be a pair (S,Φ) where S is a cyclically ordered set and Φ is an equivalence relation on S such that each equivalence class has exactly two elements. We show that each of these spaces of orderings is described by a cyclic 2-structure, in a natural way. We also show that if the real closed field R is archimedean then the space of R-places of these fields is describable in terms of the cyclic 2-structure.

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Fachgebiet (DDC)
510 Mathematik
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Orderings, Real places, Formal power series
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ISO 690KUHLMANN, Salma, Murray MARSHALL, Katarzyna OSIAK, 2011. Cyclic 2-structures and spaces of orderings of power series fields in two variables. In: Journal of Algebra. 2011, 335(1), pp. 36-48. ISSN 0021-8693. Available under: doi: 10.1016/j.jalgebra.2011.02.026
BibTex
@article{Kuhlmann2011Cycli-16744,
  year={2011},
  doi={10.1016/j.jalgebra.2011.02.026},
  title={Cyclic 2-structures and spaces of orderings of power series fields in two variables},
  number={1},
  volume={335},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={36--48},
  author={Kuhlmann, Salma and Marshall, Murray and Osiak, Katarzyna}
}
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