Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 156
On monogenity of certain number fields defined by trinomials of type $x^{2^r}+ax+b$}
Hamid Ben Yakkou
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 21, 2022
March 03, 2143
April 15, 2143

Abstract: Let $K=\mathbb{Q}(\theta)$ be a number field generated by a complex root $\theta$ of a monic irreducible trinomial $F(x) = x^{2^r}+ax+b \in \mathbb{Z}[x]$. Jhorar and Khanduja provide some explicit conditions on $a$, $b$, and $n$ for $(1, \theta, \ldots, \theta^{n-1})$ to be a power integral basis in $K$. But, if $\theta$ does not generate a power integral basis of $\mathbb{Z}_K$, then Jhorar's and Khanduja's results cannot answer on the monogenity of $K$. Also, Ben Yakkou and El Fadil studied the non-monogenity of certain number fields defined by trinomials of type $x^n+ax+b$. More ...