On quotients of the space of orderings of the field ℚ(x)

• Autorzy: Paweł Gładki , Bill Jacob
• Języki publikacji: EN

Abstrakty

EN

In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings $(X_{ℚ(x)}, G_{ℚ(x)})$ - it is, in general, nontrivial to determine whether, for a subgroup $G₀ ⊂ G_{ℚ(x)}$ the derived quotient structure $(X_{ℚ(x)}|_{G₀}, G₀)$ is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

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: Banach Center Publications
• Rocznik: 2016
• Tom: 108
• Numer: 1
• Strony: 63-84

Daty

wydano

2016

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, Mickiewicza 30, 30-059 Kraków, Poland

autor

Bill Jacob

• Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA

Identyfikatory

DOI

10.4064/bc108-0-6