Abstract

In this article, we study the monogenity of a tower of number fields defined by the iterates of a stable polynomial. We give a necessary condition for the monogenity of the number fields defined by the iterates of a stable polynomial. When the stable polynomial is of certain type, we also give a sufficient condition for the monogenity of the fields defined by each of its iterate. As a consequence, we obtain an infinite 3-tower of monogenic number fields. Moreover, we construct an infinite family of stable polynomials such that each of its iterate is non-monogenic.

中文翻译：

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多项式迭代的单调性

摘要

在本文中，我们研究由稳定多项式的迭代定义的数域塔的单调性。我们给出了由稳定多项式的迭代定义的数域的单调性的必要条件。当稳定多项式是某种类型时，我们还给出了由其每个迭代定义的域的单调性的充分条件。结果，我们得到了一个无限的单基因数域 3 塔。此外，我们构造了一个无限的稳定多项式族，使得它的每个迭代都是非单基因的。