On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two
Number Theory
2022-11-24 v3
Abstract
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 implies that the class group of 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.
Cite
@article{arxiv.2009.06464,
title = {On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two},
author = {Srilakshmi Krishnamoorthy and Sunil Kumar Pasupulati},
journal= {arXiv preprint arXiv:2009.06464},
year = {2022}
}
Comments
To appear in Archiv der Mathematik,