Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9

Rok, strany: 2023, 61 - 86

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 $\Bbb{Z}_K$, 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.: \textit{Power integral bases and monogenity of pure fields}, J. Number Theory, \textbf{173} (2017), {129–146}], where only square-free values of $m$ were considered.

ISO 690:

El Fadil, L., Gaál, I. 2023. Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9. In Tatra Mountains Mathematical Publications, vol. 83, no.1, pp. 61-86. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0006

APA:

El Fadil, L., Gaál, I. (2023). Integral bases and monogenity of pure number fields with non-square free parameters up to degree 9. Tatra Mountains Mathematical Publications, 83(1), 61-86. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0006

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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