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Quotients of index two and general quotients in a space of orderings

Volume 229 / 2015

Paweł Gładki, Murray Marshall Fundamenta Mathematicae 229 (2015), 255-275 MSC: Primary 11E10; Secondary 12D15. DOI: 10.4064/fm229-3-3

Abstract

We investigate quotient structures and quotient spaces of a space of orderings arising from subgroups of index two. We provide necessary and sufficient conditions for a quotient structure to be a quotient space that, among other things, depend on the stability index of the given space. The case of the space of orderings of the field ${\mathbb Q}(x)$ is particularly interesting, since then the theory developed simplifies significantly. A part of the theory firstly developed for quotients of index 2 generalizes to quotients of index $2^n$ for arbitrary finite $n$. Numerous examples are provided.

Authors

  • Paweł GładkiInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland
    and
    Department of Computer Science
    AGH University of Science and Technology
    al. Mickiewicza 30
    30-059 Kraków, Poland
    e-mail
  • Murray MarshallDepartment of Mathematics and Statistics
    University of Saskatchewan
    106 Wiggins Rd.
    Saskatoon, SK S7N 5E6, Canada
    e-mail

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