, Volume 94, Issue 2, pp 125-132

On cyclic biquadratic fields related to a problem of Hasse

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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.