Relative Galois module structure of integers of abelian fields
Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 1, pp. 125-141.

Let L/K be an extension of algebraic number fields, where L is abelian over . In this paper we give an explicit description of the associated order 𝒜 L/K of this extension when K is a cyclotomic field, and prove that o L , the ring of integers of L, is then isomorphic to 𝒜 L/K . This generalizes previous results of Leopoldt, Chan & Lim and Bley. Furthermore we show that 𝒜 L/K is the maximal order if L/K is a cyclic and totally wildly ramified extension which is linearly disjoint to (m ' ) /K, where m ' is the conductor of K.

Soit L/K une extension d'un corps de nombres, où L est abélienne sur . On établit ici une description explicite de l'ordre associé 𝒜 L/K de cette extension dans le cas où K est un corps cyclotomique, et on démontre que l'anneau des entiers o L de L est isomorphe à 𝒜 L/K . Cela généralise des résultats antérieurs de Leopoldt, Chan & Lim et Bley. De plus, on montre que 𝒜 L/K est l'ordre maximal si L/K est une extension cyclique, totalement et sauvagement ramifiée, linéairement disjointe de (m ' ) /K, où m ' désigne le conducteur de K.

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     title = {Relative {Galois} module structure of integers of abelian fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {125--141},
     publisher = {Universit\'e Bordeaux I},
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Byott, Nigel P.; Lettl, Günter. Relative Galois module structure of integers of abelian fields. Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 1, pp. 125-141. http://www.numdam.org/item/JTNB_1996__8_1_125_0/

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