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

Paweł Gładki; Murray Marshall

Fundamenta Mathematicae (2015)

  • Volume: 229, Issue: 3, page 255-275
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Paweł Gładki, and Murray Marshall. "Quotients of index two and general quotients in a space of orderings." Fundamenta Mathematicae 229.3 (2015): 255-275. <http://eudml.org/doc/283290>.

@article{PawełGładki2015,
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 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.},
author = {Paweł Gładki, Murray Marshall},
journal = {Fundamenta Mathematicae},
keywords = {axiomatic theory of quadratic forms; spaces of orderings; forms over real fields},
language = {eng},
number = {3},
pages = {255-275},
title = {Quotients of index two and general quotients in a space of orderings},
url = {http://eudml.org/doc/283290},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Paweł Gładki
AU - Murray Marshall
TI - Quotients of index two and general quotients in a space of orderings
JO - Fundamenta Mathematicae
PY - 2015
VL - 229
IS - 3
SP - 255
EP - 275
AB - 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.
LA - eng
KW - axiomatic theory of quadratic forms; spaces of orderings; forms over real fields
UR - http://eudml.org/doc/283290
ER -

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