Algebraic integers of pure quintic extensions

Abstract

Let $\mathbb{Q}$ denote the field of rational numbers and $\mathbb{K}$ be a pure quintic extension, that is, $\mathbb{K}=\mathbb{Q}(\sqrt[5]{d})$, where $d\in\mathbb{Z}$, $d\neq 1$ and is square free. The purpose of this work is to construct an integral basis of $\mathbb{K}$. Furthermore, we present the norm and trace of an element of $\mathbb{K}$ and the discriminant of the field $\mathbb{K}$.