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

Lhoussain El Fadil; István Gaál

doi:10.2478/tmmp-2023-0006

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

Tatra Mountains Mathematical Publications

Volume 83 (2023): Issue 1 (February 2023)

By: Lhoussain El Fadil and István Gaál

Open Access

|Mar 2023

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 ℤ_K , 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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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2023-0006 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 61 - 86

Submitted on: Nov 10, 2022

Published on: Mar 7, 2023

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

integral bases,

power integral basis,

index,

Related subjects:

© 2023 Lhoussain El Fadil, István Gaál, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 83 (2023): Issue 1 (February 2023)