# On power integral bases for certain pure number fields defined by x24 – m

@article{Fadil2020OnPI, title={On power integral bases for certain pure number fields defined by x24 – m}, author={Lhoussain El Fadil}, journal={arXiv: Number Theory}, year={2020} }

Let $K=\mathbb{Q}(\alpha)$ be a number field generated by a complex root $\alpha$ of a monic irreducible polynomial $f(x)=x^{12}-m$, with $m\neq 1$ is a square free rational integer. In this paper, we prove that if $m \equiv 2$ or $3$ (mod 4) and $m\not\equiv \mp 1$ (mod 9), then the number field $K$ is monogenic. If $m \equiv 1$ (mod 8) or $m\equiv \mp 1$ (mod 9), then the number field $K$ is not monogenic.

## 12 Citations

On power integral bases of certain pure number fields defined by $$x^{3^r} - m$$

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2021

Let $$K = \mathbb {Q} (\alpha )$$
be a pure number field generated by a root $$\alpha$$
of a monic irreducible polynomial $$F(x) = x^{3^r} -m$$
, with $$m \ne \pm 1$$
is a square-free rational…

On power integral bases of certain pure number fields defined by $$x^{42} - m$$

- MathematicsBoletín de la Sociedad Matemática Mexicana
- 2021

Let K be a pure number field generated by a complex root of a monic irreducible polynomial F(x) = x − m ∈ Z[x], with m , ±1 a square free integer. In this paper, we study the monogeneity of K. We…

On power integral bases of certain pure number fields defined by $x^{2^u\cdot3^v}-m$

- Mathematics
- 2021

Let K = Q(α) be a pure number field generated by a complex root α of a monic irreducible polynomial F(x) = x ·3 − m, with m , ±1 a square free rational integer, u, and v two positive integers. In…

On monogenity of certain pure number fields defined by $$x^{20}-m$$

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2021

Let $$K = \mathbb {Q} (\alpha )$$
be a pure number field generated by a complex root $$\alpha$$
of a monic irreducible polynomial $$F(x) = x^{20}-m$$
, with $$m \ne \mp 1$$
a square free rational…

On monogenity of certain pure number fields defined by $x^{2^u\cdot 3^v\cdot 5^t}-m$

- Mathematics
- 2022

A bstract . Let K = Q ( α ) be a pure number ﬁeld generated by a root α of a monic irreducible polynomial F ( x ) = x 2 u · 3 v · 5 t − m , with m , ± 1 a square free rational integer, u , v and t…

On power integral bases for certain pure number fields defined by

- Mathematics
- 2020

Abstract Let be a pure number field generated by a root α of a monic irreducible polynomial with is a square free integer, r and s are two positive integers. In this article, we study the monogenity…

On monogenity of certain number fields defined by trinomials

- Mathematics
- 2021

Let K = Q(θ) be a number field generated by a complex root θ of a monic irreducible trinomial F (x) = x + ax + b ∈ Z[x]. There is an extensive literature of monogenity of number fields defined by…

ON MONOGENITY OF CERTAIN NUMBER FIELDS DEFINED BY TRINOMIALS

- Mathematics
- 2021

. Let K = Q ( θ ) be a number ﬁeld generated by a complex root θ of a monic irreducible trinomial F ( x ) = x n + ax + b ∈ Z [ x ] . There is an extensive literature of monogenity of number ﬁelds…

A note ON MONOGENEITY of pure number fields

- Mathematics
- 2021

Gassert’s paper ”A NOTE ON THE MONOGENEITY OF POWER MAPS” is cited at least by 17 papers in the context of monogeneity of pure number fields despite some errors that it contains and remarks on it. In…

On monogenity of certain number fields defined by $$x^8+ax+b$$

- MathematicsActa Mathematica Hungarica
- 2022

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