Biquadratic fields having a non-principal euclidean ideal class
Abstract
H. W. Lenstra lenstra introduced the notion of an Euclidean ideal class, which is a generalization of norm-Euclidean ideals in number fields. Later, families of number fields of small degree were obtained with an Euclidean ideal class (for instance, in hester1 and cathy). In this paper, we construct certain new families of biquadratic number fields having a non-principal Euclidean ideal class and this extends the previously known families given by H. Graves hester1 and C. Hsu cathy.
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