An -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.

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's solution of Hilbert'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},
     volume = {Ser. 6, 19},
     number = {S1},
     year = {2010},
     doi = {10.5802/afst.1282},
     mrnumber = {2675728},
     zbl = {pre05799088},
     language = {en},
     url = {www.numdam.org/item/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://www.numdam.org/item/AFST_2010_6_19_S1_215_0/

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