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

Paweł Gładki, and Bill Jacob. "On quotients of the space of orderings of the field ℚ(x)." Banach Center Publications 108.1 (2016): 63-84. <http://eudml.org/doc/286488>.

@article{PawełGładki2016,
abstract = {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.},
author = {Paweł Gładki, Bill Jacob},
journal = {Banach Center Publications},
keywords = {space of orderings; Lam's open problem},
language = {eng},
number = {1},
pages = {63-84},
title = {On quotients of the space of orderings of the field ℚ(x)},
url = {http://eudml.org/doc/286488},
volume = {108},
year = {2016},
}

TY - JOUR
AU - Paweł Gładki
AU - Bill Jacob
TI - On quotients of the space of orderings of the field ℚ(x)
JO - Banach Center Publications
PY - 2016
VL - 108
IS - 1
SP - 63
EP - 84
AB - 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.
LA - eng
KW - space of orderings; Lam's open problem
UR - http://eudml.org/doc/286488
ER -