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arXiv · 2408.14524

On characterization of prime divisors of the index of a quadrinomial

Tapas Chatterjee·Karishan Kumar
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Abstract

Let $\theta$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $\theta$ over the rationals. Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we characterize all the prime divisors of the discriminant of $f(x)$ which do not divide the index of $f(x).$ As a fascinating corollary, we deduce necessary and sufficient conditions for the monogenity of the field $K=\mathbb{Q}(\theta),$ where $\theta$ is associated with certain quadrinomials.

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Tapas Chatterjee, Karishan Kumar. 2024-08-26. On characterization of prime divisors of the index of a quadrinomial. https://arxiv.org/abs/2408.14524

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