We prove that a certain class of biquadratic fields have a Euclidean ideal.Comment: 10 page

Pasupulati, Sunil Kumar

English

arXiv

Lenstra introduced the notion of a Euclidean ideal class, which is a
generalization of the Euclidean domain. Lenstra also proved that the Euclidean
ideal in a number field $K$ implies that the class group of $K$ is cyclic. We
construct a family of biquadratic fields with a Euclidean ideal whenever the
class number is 2. This extends the families given by Graves, Hsu,
Chattopadhyay, and Muthukrishnan.Comment: To appear in Archiv der Mathematik

On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two

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