Quotients of index two and general quotients
in a space of orderings
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.
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
Affiliations des auteurs :
Paweł Gładki 1 ; Murray Marshall 2
@article{10_4064_fm229_3_3,
author = {Pawe{\l} G{\l}adki and Murray Marshall},
title = {Quotients of index two and general quotients
in a space of orderings},
journal = {Fundamenta Mathematicae},
pages = {255--275},
publisher = {mathdoc},
volume = {229},
number = {3},
year = {2015},
doi = {10.4064/fm229-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm229-3-3/}
}
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 SP - 255 EP - 275 VL - 229 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm229-3-3/ DO - 10.4064/fm229-3-3 LA - en ID - 10_4064_fm229_3_3 ER -
%0 Journal Article %A Paweł Gładki %A Murray Marshall %T Quotients of index two and general quotients in a space of orderings %J Fundamenta Mathematicae %D 2015 %P 255-275 %V 229 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/fm229-3-3/ %R 10.4064/fm229-3-3 %G en %F 10_4064_fm229_3_3
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
Cité par Sources :