## Tokyo Journal of Mathematics

### On Unramified Galois Extensions of Certain Algebraic Number Fields

#### 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 $n\in\mathbf{Z}$.

#### Article information

Source
Tokyo J. Math., Volume 16, Number 2 (1993), 351-354.

Dates
First available in Project Euclid: 1 April 2010

https://projecteuclid.org/euclid.tjm/1270128489

Digital Object Identifier
doi:10.3836/tjm/1270128489

Mathematical Reviews number (MathSciNet)
MR1247658

Zentralblatt MATH identifier
0802.11049

#### Citation

KOMATSU, Kenzo; NODERA, Takashi. On Unramified Galois Extensions of Certain Algebraic Number Fields. Tokyo J. Math. 16 (1993), no. 2, 351--354. doi:10.3836/tjm/1270128489. https://projecteuclid.org/euclid.tjm/1270128489