On index divisors and monogenity of certain octic number fields defined by $x^8+ax^3+b$

• Date: 2024
• Main Author: Kchit, Omar
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7536
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 511 For any octic number field $K$ generated by a root $\alpha$ of a monic irreducible trinomial $F(x)=x^8+ax^3+b \in \mathbb{Z}[x]$ and for every rational prime $p,$ we show when $p$ divides the index of $K.$  We also describe the prime power decomposition of the index...