Annales Mathematiques Africaines


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Generators of power integral bases of MATH



François E. TANOE*
Kouassi Vincent KOUAKOU**

UFR Mathématiques - Informatique Université Félix Boigny,
22 BP 582 Abidjan 22, Côte d'Ivoire




Mathematics Subject Classification: (2010) 11R60
Key words : cyclotomic field

Abstract:


The cyclotomic field MATH is the single monogenic $m-$quadratic number fields$:$
MATH when $m\geq 3, $ ($i.e$ compositum of $m$ quadratic number fields ). In this paper we determine all the generators of power integral bases of MATH by using a system of diophantine equations. We find that these generators are exactly the eigth conjugates of $\zeta _{24}$ modulo $\U{2124} .$

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