Non-monogenity of certain octic number fields defined by trinomials
Volume 171 / 2023
Colloquium Mathematicum 171 (2023), 145-152
MSC: Primary 11R04; Secondary 11R21.
DOI: 10.4064/cm8799-3-2022
Published online: 28 July 2022
Abstract
Let $K=\mathbb Q(\theta )$ be an algebraic number field with $\theta $ a root of an irreducible polynomial $f(x)=x^8+ax^m+b\in \mathbb Z[x]$ and $1\leq m \leq 7$. We study the monogenity of $K$. Precisely, we give some explicit conditions on $a,b$ for which $K$ is non-monogenic. As an application of our results, we provide some classes of algebraic number fields which are non-monogenic. Finally, we illustrate our results through examples.
