TY - JOUR
T1 - On power bases in cyclotomic number fields
AU - Bremner, Andrew
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1988/3
Y1 - 1988/3
N2 - The current paper considers the question of power bases in the cyclotomic number field Q(ζ), ζp = 1, p an odd prime. The ring of integers is Z[ζ], and there do exist further "non-obvious" generators for this order; specifically we shall see that Z[α] = Z[ζ] for α = ζ + ζ2 + ⋯ + ζ (p-1) 2. We conjecture that, up to conjugacy, there can be no further such integral generators, and prove that this is indeed the case in Q(ζ7).
AB - The current paper considers the question of power bases in the cyclotomic number field Q(ζ), ζp = 1, p an odd prime. The ring of integers is Z[ζ], and there do exist further "non-obvious" generators for this order; specifically we shall see that Z[α] = Z[ζ] for α = ζ + ζ2 + ⋯ + ζ (p-1) 2. We conjecture that, up to conjugacy, there can be no further such integral generators, and prove that this is indeed the case in Q(ζ7).
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U2 - 10.1016/0022-314X(88)90044-3
DO - 10.1016/0022-314X(88)90044-3
M3 - Article
AN - SCOPUS:38249028372
SN - 0022-314X
VL - 28
SP - 288
EP - 298
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 3
ER -