2021/10/01 by Srilakshmi Krishnamoorthy, Krishnamoorthy, Srilakshmi, Sunil Kumar Pasupulati +1 · 1 citation
Mathematics · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2110.00225
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.