Geodesic
Quotients of index two and general quotients in a space of orderings
Paweł Gładki1 ; Murray Marshall2
1 Institute 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
2 Department of Mathematics and Statistics University of Saskatchewan 106 Wiggins Rd. Saskatoon, SK S7N 5E6, Canada
Fundamenta Mathematicae, Tome 229 (2015) no. 3, pp. 255-275.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm229-3-3
Keywords: investigate quotient structures quotient spaces space orderings arising subgroups index provide necessary sufficient conditions quotient structure quotient space among other things depend stability index given space the space orderings field mathbb particularly interesting since theory developed simplifies significantly part theory firstly developed quotients index generalizes quotients index arbitrary finite numerous examples provided

Paweł Gładki 1 ; Murray Marshall 2

1 Institute 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
2 Department of Mathematics and Statistics University of Saskatchewan 106 Wiggins Rd. Saskatoon, SK S7N 5E6, Canada 
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Paweł Gładki; Murray Marshall. Quotients of index two and general quotients
 in a space of orderings. Fundamenta Mathematicae, Tome 229 (2015) no. 3, pp. 255-275. doi : 10.4064/fm229-3-3. http://geodesic.mathdoc.fr/articles/10.4064/fm229-3-3/

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