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arXiv · 2110.00225

Low degree extensions with Cyclic class group

Srilakshmi Krishnamoorthy·Sunil Kumar Pasupulati
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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.

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Srilakshmi Krishnamoorthy, Sunil Kumar Pasupulati. 2021-10-01. Low degree extensions with Cyclic class group. https://arxiv.org/abs/2110.00225

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