On monogenity of certain pure number fields of degrees 2 r · 3 k · 7 s

Hamid Ben Yakkou; Jalal Didi

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 2, page 167-183
  • ISSN: 0862-7959

Abstract

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Let K = ℚ ( α ) be a pure number field generated by a complex root α of a monic irreducible polynomial F ( x ) = x 2 r · 3 k · 7 s - m ∈ 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.

How to cite

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Ben Yakkou, Hamid, and Didi, Jalal. "On monogenity of certain pure number fields of degrees $2^r\cdot 3^k\cdot 7^s$." Mathematica Bohemica 149.2 (2024): 167-183. <http://eudml.org/doc/299586>.

@article{BenYakkou2024,
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\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.},
author = {Ben Yakkou, Hamid, Didi, Jalal},
journal = {Mathematica Bohemica},
keywords = {power integral basis; theorem of Ore; prime ideal factorization; common index divisor},
language = {eng},
number = {2},
pages = {167-183},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On monogenity of certain pure number fields of degrees $2^r\cdot 3^k\cdot 7^s$},
url = {http://eudml.org/doc/299586},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Ben Yakkou, Hamid
AU - Didi, Jalal
TI - On monogenity of certain pure number fields of degrees $2^r\cdot 3^k\cdot 7^s$
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 2
SP - 167
EP - 183
AB - 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.
LA - eng
KW - power integral basis; theorem of Ore; prime ideal factorization; common index divisor
UR - http://eudml.org/doc/299586
ER -

References

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