论文标题
相对理想的任意秩序类别
Relative Ideal Classes of Arbitrary Order
论文作者
论文摘要
我们适应已知的技术来搜索理想的任意顺序，然后将其应用于三个数字领域的家庭。我们表明，一个循环六号数字的家族中有许多字段，其中包含相对理想的订单$ r类，其中$ r $是一个积极的整数，相对于扩展程度。然后，我们表明，对于一个循环四分之一的数字字段而言，情况也是如此。尽管该技术传统上是应用于Galois扩展名的，但我们展示了如何适应它来处理非Galois Cubic数字领域的家庭，并证明该家族包含了许多具有理想的任意秩序相对较高质量为三个的领域。
We adapt a known technique for searching for ideal classes of arbitrary order and then apply it to three families of number fields. We show that a family of cyclic sextic number fields has infinitely many fields in it that contain a relative ideal class of order $r,$ where $r$ is a positive integer relatively prime to the degree of the extension. We then show that the same holds true for a family of cyclic quartic number fields. Though the technique is traditionally applied to Galois extensions, we show how it may be adapted to handle a family of non-Galois cubic number fields and prove that this family contains infinitely many fields with an ideal class of arbitrary order relatively prime to three.
