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

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	351-354
Number of pages	4
Journal	Tokyo Journal of Mathematics
Volume	16
Issue number	2
DOIs	https://doi.org/10.3836/tjm/1270128489
Publication status	Published - 1993 Dec
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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title = "On unramified galois extensions of certain algebraic number fields",

abstract = "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.",

author = "Kenzo Komatsu and Takashi Nodera",

year = "1993",

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AU - Nodera, Takashi

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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

Abstract

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