The Joly–Becker theorem for * –orderings

Igor Klep[1]; Dejan Velušček[2]

  • [1] Univerza v Ljubljani, Oddelek za matematiko Inštituta za matematiko, fiziko in mehaniko, Jadranska 19, SI–1111 Ljubljana, Slovenia
  • [2] University of Ljubljana, Faculty of Mathematics and Physics, Department of Mathematics, Jadranska 19, SI–1000 Ljubljana, Slovenia.

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 1, page 81-92
  • ISSN: 0240-2963

Abstract

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We prove the * –version of the Joly–Becker theorem: a skew field admits a * –ordering of level n iff it admits a * –ordering of level n ℓ for some (resp. all) odd ℓ ∈ ℕ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a * –ordering of higher level also admits a * –ordering of level 1 . Every field that admits a * –ordering of higher level admits a * –ordering of level 1 or 2

How to cite

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Klep, Igor, and Velušček, Dejan. "The Joly–Becker theorem for $*$–orderings." Annales de la faculté des sciences de Toulouse Mathématiques 17.1 (2008): 81-92. <http://eudml.org/doc/10083>.

@article{Klep2008,
abstract = {We prove the $*$–version of the Joly–Becker theorem: a skew field admits a $*$–ordering of level $n$ iff it admits a $*$–ordering of level $n \ell $ for some (resp. all) odd $\ell \in \mathbb\{N\}$. For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a $*$–ordering of higher level also admits a $*$–ordering of level $1$. Every field that admits a $*$–ordering of higher level admits a $*$–ordering of level $1$ or $2$},
affiliation = {Univerza v Ljubljani, Oddelek za matematiko Inštituta za matematiko, fiziko in mehaniko, Jadranska 19, SI–1111 Ljubljana, Slovenia; University of Ljubljana, Faculty of Mathematics and Physics, Department of Mathematics, Jadranska 19, SI–1000 Ljubljana, Slovenia.},
author = {Klep, Igor, Velušček, Dejan},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {6},
number = {1},
pages = {81-92},
publisher = {Université Paul Sabatier, Toulouse},
title = {The Joly–Becker theorem for $*$–orderings},
url = {http://eudml.org/doc/10083},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Klep, Igor
AU - Velušček, Dejan
TI - The Joly–Becker theorem for $*$–orderings
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 1
SP - 81
EP - 92
AB - We prove the $*$–version of the Joly–Becker theorem: a skew field admits a $*$–ordering of level $n$ iff it admits a $*$–ordering of level $n \ell $ for some (resp. all) odd $\ell \in \mathbb{N}$. For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a $*$–ordering of higher level also admits a $*$–ordering of level $1$. Every field that admits a $*$–ordering of higher level admits a $*$–ordering of level $1$ or $2$
LA - eng
UR - http://eudml.org/doc/10083
ER -

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