A generalization of simplest number fields and their integral basis

TL;DR

This paper generalizes the concept of simplest number fields to arbitrary degrees and demonstrates that their integral bases exhibit a repeating periodic pattern, expanding understanding of their algebraic structure.

Contribution

It introduces a generalization of simplest number fields to any degree and proves that their integral bases are periodic, extending prior specific degree cases.

Findings

Integral bases of generalized simplest number fields are periodic.

The periodicity pattern applies to fields of any degree.

Provides a unified framework for understanding these number fields.

Abstract

An integral basis of the simplest number fields of degree 3,4 and 6 over $\mathbb{Q}$ are well-known, and widely investigated. We generalize the simplest number fields to any degree, and show that an integral basis of these fields is repeating periodically.