REAL QUADRATIC EXTENSIONS OF THE RATIONAL FUNCTION FIELD IN CHARACTERISTIC TWO by
نویسندگان
چکیده
— We consider real quadratic extensions of the rational field over a finite field of characteristic two. After recalling the equation of such extensions, we present a geometric approach of the continued fraction expansion algorithm to compute the regulator. Finally, we study the ideal class number one problem and give numerous examples for which the ideal class number equals one. Résumé (Extensions quadratiques réelles du corps rationnel en caractéristique 2) Nous étudions les extensions quadratiques réelles du corps rationnel sur un corps fini de caractéristique 2. On rappelle la forme générale de telles extensions puis on donne une approche géométrique de l’algorithme des fractions continues qui permet de calculer le régulateur. Enfin on s’intéresse aux extensions quadratiques réelles dont le nombre de classes d’idéaux de l’anneau des entiers est égal à un et on donne un grand nombre d’exemples pour lesquels cette situation est réalisée.
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