多项式迭代的同源性

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-01-16 DOI:10.1007/s00013-023-01949-9

Himanshu Sharma, Ritumoni Sarma, Shanta Laishram

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引用次数: 0

摘要

摘要本文研究由稳定多项式迭代定义的数域塔的单原性。我们给出了由稳定多项式迭代定义的数域单原性的必要条件。当稳定多项式是某种类型时，我们还给出了它的每个迭代数所定义数域的单原性的充分条件。因此，我们得到了单源数域的无限 3 塔。此外，我们还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源的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Monogenity of iterates of polynomials

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.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.