Let be an extension of algebraic number fields, where is abelian over . In this paper we give an explicit description of the associated order of this extension when is a cyclotomic field, and prove that , the ring of integers of , is then isomorphic to . This generalizes previous results of Leopoldt, Chan & Lim and Bley. Furthermore we show that is the maximal order if is a cyclic and totally wildly ramified extension which is linearly disjoint to , where is the conductor of .
Soit une extension d'un corps de nombres, où est abélienne sur . On établit ici une description explicite de l'ordre associé de cette extension dans le cas où est un corps cyclotomique, et on démontre que l'anneau des entiers de est isomorphe à . Cela généralise des résultats antérieurs de Leopoldt, Chan & Lim et Bley. De plus, on montre que est l'ordre maximal si est une extension cyclique, totalement et sauvagement ramifiée, linéairement disjointe de , où désigne le conducteur de .
@article{JTNB_1996__8_1_125_0, author = {Nigel P. Byott and G\"unter Lettl}, 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}, volume = {8}, number = {1}, year = {1996}, doi = {10.5802/jtnb.160}, zbl = {0859.11059}, mrnumber = {1399950}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.160/} }
TY - JOUR TI - Relative Galois module structure of integers of abelian fields JO - Journal de Théorie des Nombres de Bordeaux PY - 1996 DA - 1996/// SP - 125 EP - 141 VL - 8 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.160/ UR - https://zbmath.org/?q=an%3A0859.11059 UR - https://www.ams.org/mathscinet-getitem?mr=1399950 UR - https://doi.org/10.5802/jtnb.160 DO - 10.5802/jtnb.160 LA - en ID - JTNB_1996__8_1_125_0 ER -
Nigel P. Byott; Günter Lettl. Relative Galois module structure of integers of abelian fields. Journal de Théorie des Nombres de Bordeaux, Volume 8 (1996) no. 1, pp. 125-141. doi : 10.5802/jtnb.160. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.160/
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