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

• Autorzy: Paweł Gładki , Murray Marshall
• Języki publikacji: EN

Abstrakty

EN

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 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 2ⁿ for arbitrary finite n. Numerous examples are provided.

Kategorie tematyczne

• 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
• 11E10: Forms over real fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 229
• Numer: 3
• Strony: 255-275

Daty

wydano

2015

Twórcy

autor

Paweł Gładki

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
• Department of Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Murray Marshall

• Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Rd., Saskatoon, SK S7N 5E6, Canada

Identyfikatory

DOI

10.4064/fm229-3-3