Geodesic
On monogenity of certain pure number fields of degrees $2^r\cdot 3^k\cdot 7^s$
Mathematica Bohemica, Tome 149 (2024) no. 2, pp. 167-183
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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\cdot 3^k\cdot 7^s} -m \in \mathbb{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.
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\cdot 3^k\cdot 7^s} -m \in \mathbb{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.
DOI : 10.21136/MB.2023.0071-22
Classification : 11R04, 11R16, 11R21
Keywords: power integral basis; theorem of Ore; prime ideal factorization; common index divisor 
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Ben Yakkou, Hamid; Didi, Jalal. On monogenity of certain pure number fields of degrees $2^r\cdot 3^k\cdot 7^s$. Mathematica Bohemica, Tome 149 (2024) no. 2, pp. 167-183. doi: 10.21136/MB.2023.0071-22

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