On rings of integers generated by their units

TL;DR

This paper proves that every number field has a finite extension whose ring of integers is generated by units, extending previous results and generalizing a theorem on power-free polynomial values.

Contribution

It provides an affirmative answer to a question about rings of integers generated by units and generalizes a theorem on power-free polynomial values in number fields.

Findings

Every number field has a finite extension with ring of integers generated by units

Generalization of Hinz's theorem on power-free polynomial values

Advances understanding of algebraic number fields and their units

Abstract

We give an affirmative answer to the following question by Jarden and Narkiewicz: Is it true that every number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)? As a part of the proof, we generalize a theorem by Hinz on power-free values of polynomials in number fields.