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December 1993 On Unramified Galois Extensions of Certain Algebraic Number Fields
Kenzo KOMATSU, Takashi NODERA
Tokyo J. Math. 16(2): 351-354 (December 1993). DOI: 10.3836/tjm/1270128489

Abstract

Let $a\in\mathbf{Z}$ such that $a\neq 1$, $a\neq-2^{17}$ and $(17,a)=1$. Let $\alpha_1,\alpha_2,\ldots,\alpha_{17}$ denote the roots of $x^{17}+ax+a=0$. It is shown that every prime ideal is unramified in $\mathbf{Q}(\alpha_1,\alpha_2,\ldots,\alpha_{17})/\mathbf{Q}(\alpha_1)$ if and only if $a=2^{62}n^2+4605612312119580521n+1149886651258880054$ for some $n\in\mathbf{Z}$.

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Kenzo KOMATSU. Takashi NODERA. "On Unramified Galois Extensions of Certain Algebraic Number Fields." Tokyo J. Math. 16 (2) 351 - 354, December 1993. https://doi.org/10.3836/tjm/1270128489

Information

Published: December 1993
First available in Project Euclid: 1 April 2010

zbMATH: 0802.11049
MathSciNet: MR1247658
Digital Object Identifier: 10.3836/tjm/1270128489

Rights: Copyright © 1993 Publication Committee for the Tokyo Journal of Mathematics

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Vol.16 • No. 2 • December 1993
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