English

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

Number Theory 2023-03-02 v2

Abstract

For a number field KK defined by a trinomail F(x)=x7+ax+bZ[x]F(x) = x^7+ax+b \in \mathbb{Z}[x], Jakhar and Kumar gave some necessary conditions on aa and bb, which guarantee the non-monogenity of KK \cite{A6}. In this paper, for every prime integer pp, we characterize when pp is a common index divisor of KK. In particular, if any one of these conditions holds, then KK is not monogenic. In such a way our proposed results extend those of Jakhar and Kumar.

Keywords

Cite

@article{arxiv.2202.09342,
  title  = {On index divisors and monogenity of certain number fields defined by trinomials $x^7+ax+b$},
  author = {Lhoussain El Fadil},
  journal= {arXiv preprint arXiv:2202.09342},
  year   = {2023}
}

Comments

Submitted. arXiv admin note: substantial text overlap with arXiv:2112.01133