9次以下非平方自由参数纯数域的积分基与单性

Q4 Mathematics

Tatra Mountains Mathematical Publications Pub Date : 2023-02-01 DOI:10.2478/tmmp-2023-0006

L. El Fadil, István Gaál

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引用次数: 0

摘要

摘要设K是一个单不可约多项式f（x）=xn−m的根α生成的纯数域，其中m是有理整数，3≤n≤9是整数。在本文中，我们计算了ℤK，我们研究了K的单胚性，将以前的结果推广到m不一定是无平方的情况。在这种更普遍的情况下，收集并完成相应的结果，我们的目的是提供一个类似于[Gaál，I.--Remete，l.:纯域的幂积分基和单胚性，J.Number Theory，173（2017），129–146]的结果，其中只考虑了m的无平方值。

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Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

Abstract Let K be a pure number field generated by a root α of a monic irreducible polynomial f (x)= xn − m with m a rational integer and 3 ≤ n ≤ 9 an integer. In this paper, we calculate an integral basis of ℤK , and we study the monogenity of K, extending former results to the case when m is not necessarily square-free. Collecting and completing the corresponding results in this more general case, our purpose is to provide a parallel to [Gaál, I.—Remete, L.: Power integral bases and monogenity of pure fields,J.Number Theory, 173 (2017), 129–146], where only square-free values of m were considered.

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来源期刊

Tatra Mountains Mathematical Publications Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量