Mathematica Bohemica, Vol. 149, No. 2, pp. 167-183, 2024


On monogenity of certain pure number fields of degrees $2^r\cdot3^k\cdot7^s$

Hamid Ben Yakkou, Jalal Didi

Received May 29, 2022.   Published online March 27, 2023.

Abstract:  Let $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a complex root $\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^r\cdot3^k\cdot7^s} -m \in\bb{Z}[x]$, where $r$, $k$, $s$ are three positive natural integers. The purpose of this paper is to study the monogenity of $K$. Our results are illustrated by some examples.
Keywords:  power integral basis; theorem of Ore; prime ideal factorization; common index divisor
Classification MSC:  11R04, 11R16, 11R21

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Affiliations:   Hamid Ben Yakkou (corresponding author), Jalal Didi, Faculty of Sciences Dhar El Mahraz, P.O. Box 1874, Fez, Sidi Mohamed Ben Abdellah University, Morocco, e-mail: beyakouhamid@gmail.com, didimath1992@live.fr


 
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