On unramified galois extensions of certain algebraic number fields

Kenzo Komatsu; Takashi Nodera

doi:10.3836/tjm/1270128489

On unramified galois extensions of certain algebraic number fields

Kenzo Komatsu
, Takashi Nodera

研究成果: Article › 査読

抄録

Let a∈Z such that a≠1, a≠−2¹⁷ and (17,a)=1. Let α₁,α₂,…,α₁₇ denote the roots of x¹⁷+ax+a=0. It is shown that every prime ideal is unramified in Q(α₁,α₂,…,α₁₇)/Q(α₁) if and only if a=2⁶²n²+4605612312119580521n+1149886651258880054 for some n∈Z.

本文言語	English
ページ（範囲）	351-354
ページ数	4
ジャーナル	Tokyo Journal of Mathematics
巻	16
号	2
DOI	https://doi.org/10.3836/tjm/1270128489
出版ステータス	Published - 1993 12月
外部発表	はい

ASJC Scopus subject areas

数学一般

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10.3836/tjm/1270128489

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AB - Let a∈Z such that a≠1, a≠−217 and (17,a)=1. Let α1,α2,…,α17 denote the roots of x17+ax+a=0. It is shown that every prime ideal is unramified in Q(α1,α2,…,α17)/Q(α1) if and only if a=262n2+4605612312119580521n+1149886651258880054 for some n∈Z.

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On unramified galois extensions of certain algebraic number fields

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