First-degree prime ideals of Z[alpha+beta] can be combined from those of Z[alpha] and Z[beta], but the claimed preservation of divisibility of principal ideals rests on a false intersection formula.
A new family of biquadratic fields having a non-principal euclidean ideal class
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abstract
In this paper, based on the theory of genus fields of biquadartic fields, we find a new larger family of biquadratic fields having a non-principal Euclidean ideal class, which implies the main results of \cite{JNT}.
fields
math.NT 1years
2019 1verdicts
REJECT 1representative citing papers
citing papers explorer
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First-Degree Prime Ideals of Biquadratic Fields dividing prescribed Principal Ideals
First-degree prime ideals of Z[alpha+beta] can be combined from those of Z[alpha] and Z[beta], but the claimed preservation of divisibility of principal ideals rests on a false intersection formula.