论文标题
关于在二等级的双Quadratic领域中存在非主要欧几里得理想班
On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two
论文作者
论文摘要
Lenstra引入了欧几里得理想类别的概念，这是欧几里得领域的概括。 Lenstra还证明了数字字段$ k $中的欧几里得理想意味着$ k $的类是循环的。每当班级数为2时，我们都会建立一个具有欧几里得理想的二次阶级场的家庭。这扩展了Graves，Hsu，Chattopadhyay和Muthukrishnan的家族。
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 $K$ implies that the class group of $K$ 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.
