En utilisant les algèbres réticulées, on montre qu’un corps totalement ordonné qui a un unique ordre total et qui est dense dans sa clôture réelle a la propriété que chacune des ses fonctions rationnelles positives semi-définies est une somme de carrés.
Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.
@article{AFST_2010_6_19_S1_215_0,
author = {Steinberg, Stuart A.},
title = {An $\ell $-algebra approach to {Artin{\textquoteright}s} solution of {Hilbert{\textquoteright}s} {Seventeenth} {Problem}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {215--220},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 19},
number = {S1},
year = {2010},
doi = {10.5802/afst.1282},
mrnumber = {2675728},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1282/}
}
TY - JOUR AU - Steinberg, Stuart A. TI - An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2010 SP - 215 EP - 220 VL - 19 IS - S1 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1282/ DO - 10.5802/afst.1282 LA - en ID - AFST_2010_6_19_S1_215_0 ER -
%0 Journal Article %A Steinberg, Stuart A. %T An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 215-220 %V 19 %N S1 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1282/ %R 10.5802/afst.1282 %G en %F AFST_2010_6_19_S1_215_0
Steinberg, Stuart A. An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. S1, pp. 215-220. doi : 10.5802/afst.1282. http://archive.numdam.org/articles/10.5802/afst.1282/
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