Générateurs de l'anneau des entiers d'une extension cyclotomique

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• 作者：Gabriele Ranieri
• 关键词：Cyclotomic ; Power bases ; Bremner's conjecture
• 刊名：Journal of Number Theory
• 出版年：2008
• 出版时间：June 2008
• 年：2008
• 卷：128
• 期：6
• 页码：1576-1586
• 全文大小：137 K

文摘

Let p be an odd prime and q=p^m, where m is a positive integer. Let ζ_q be a qth primitive root of 1 and be the ring of integers in . In [I. Gaál, L. Robertson, Power integral bases in prime-power cyclotomic fields, J. Number Theory 120 (2006) 372–384] I. Gaál and L. Robertson show that if 52c4d7"">, where is the class number of , then if is a generator of (in other words ) either is equals to a conjugate of an integer translate of ζ_q or is an odd integer. In this paper we show that we can remove the hypothesis over . In other words we show that if is a generator of c40b28aea""> then either is a conjugate of an integer translate of ζ_q or is an odd integer.