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arXiv · 2202.09342

On index divisors and monogenity of certain number fields defined by trinomials $x^7+ax+b$

Lhoussain El Fadil
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Abstract

For a number field $K$ defined by a trinomail $F(x) = x^7+ax+b \in \mathbb{Z}[x]$, Jakhar and Kumar gave some necessary conditions on $a$ and $b$, which guarantee the non-monogenity of $K$ \cite{A6}. In this paper, for every prime integer $p$, we characterize when $p$ is a common index divisor of $K$. In particular, if any one of these conditions holds, then $K$ is not monogenic. In such a way our proposed results extend those of Jakhar and Kumar.

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Lhoussain El Fadil. 2022-02-18. On index divisors and monogenity of certain number fields defined by trinomials $x^7+ax+b$. https://arxiv.org/abs/2202.09342

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