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We explain how it is possible to construct explicit sums of squares by deciphering an abstract proof giving a positive answer to the 17th Hilbert’s Problem. When doing this job we replace abstract objects in the classical proof by incomplete specifications of these objects. Key-words : 17–th Hilbert problem. Artin-Schreier Theory. Constructive mathematics . Hilbert Program. MSC 2000 : 03F65, 03B35, 12D15, 12J15, 14Q20

publications mathématiques de l'université de franche-comté besançon. algèbre et théorie des nombres/publications mathématiques de besançon. algèbre et théorie des nombres

Constructions cachées en algèbre abstraite (4). La solution du 17e problème de Hilbert par la théorie d’Artin-Schreier