Low degree extensions with Cyclic class group
Number Theory
2025-04-28 v2
Abstract
Lenstra introduced the notion of the Euclidean ideal class, a generalization of the Euclidean domain that captures cyclic class groups. In this article, we establish the existence of Euclidean ideal classes in abelian quartic fields. As a corollary, we demonstrate that certain biquadratic fields with class number two possess a Euclidean ideal class. Additionally, we investigate the presence of Euclidean ideal classes in specific cubic and quadratic extensions.
Cite
@article{arxiv.2110.00225,
title = {Low degree extensions with Cyclic class group},
author = {Srilakshmi Krishnamoorthy and Sunil Kumar Pasupulati},
journal= {arXiv preprint arXiv:2110.00225},
year = {2025}
}