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The Joly–Becker theorem for *–orderings
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 81-92.

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 for some (resp. all) odd . 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

Nous démontrons la version involutive du théorème de Joly et Becker : une algèbre à division admet un ordre involutif de niveau n si et seulement si elle admet un ordre involutif de niveau n pour un certain (puis tout) impair . Dans le cas d’une algèbre à division avec une unité imaginaire ou d’un corps commutatif, nous présentons des résultats plus forts : si une algèbre à division avec unité imaginaire admet un ordre involutif de niveau supérieur, elle admet aussi un ordre involutif de niveau 1. Tout corps admettant un ordre involutif de niveau supérieur admet un ordre involutif de niveau 1 ou 2.

DOI: 10.5802/afst.1177
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.
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     title = {The {Joly{\textendash}Becker} theorem for $*${\textendash}orderings},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {81--92},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
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Igor Klep; Dejan Velušček. The Joly–Becker theorem for $*$–orderings. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 81-92. doi : 10.5802/afst.1177. https://afst.centre-mersenne.org/articles/10.5802/afst.1177/

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