TY - JOUR
T1 - On unramified galois extensions of certain algebraic number fields
AU - Komatsu, Kenzo
AU - Nodera, Takashi
PY - 1993/12
Y1 - 1993/12
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=84972515119&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84972515119&partnerID=8YFLogxK
U2 - 10.3836/tjm/1270128489
DO - 10.3836/tjm/1270128489
M3 - Article
AN - SCOPUS:84972515119
SN - 0387-3870
VL - 16
SP - 351
EP - 354
JO - Tokyo Journal of Mathematics
JF - Tokyo Journal of Mathematics
IS - 2
ER -