Abstract
In this note we shall prove that there exist infinitely many cyclic biquadratic fieldsK whose integral bases are neither {1, α, α2, β} nor {1, α, β, α3) for any numbers α, β inK. Next, we shall construct infinitely many cyclic biquadratic fieldsK which have the index 1, but still have not the integral basis {1, α, α2, α3) for every α inK. Finally we shall give a class of biquadratic fields for a problem of Hasse concerning an integral basis.
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Nakahara, T. On cyclic biquadratic fields related to a problem of Hasse. Monatshefte für Mathematik 94, 125–132 (1982). https://doi.org/10.1007/BF01301930
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DOI: https://doi.org/10.1007/BF01301930