Non-principal Euclidean ideal class in a family of biquadratic fields with the class number two

被引：0

作者：

Srilakshmi Krishnamoorthy

Sunil Kumar Pasupulati

机构：

[1] Indian Institute of Science Education and Research,

来源：

Archiv der Mathematik | 2023年 / 120卷

关键词：

Euclidean algorithm for number fields; Artin symbol; Euclidean ideal class; Ideal class group; Hilbert class field; Primary 11A05; Secondary 11R29;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Lenstra introduced the notion of a Euclidean ideal class, which is a generalization of the Euclidean domain. Lenstra also proved that the existence of a Euclidean ideal in a number field K implies that the class group of K is cyclic. We construct a family of biquadratic fields that have a Euclidean ideal whenever the class number is 2. This extends the families given by Graves, Hsu, Chattopadhyay and Muthukrishnan.

引用

页码：263 / 271

页数：8

共 16 条

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