On rings of integers generated by 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.

15 pages

References in corpus (2)

• Sums of units in function fields
• Sums of units in function fields II - The extension problem

Cited by in corpus (5)

• Additive unit representations in global fields - A survey
• Twisted conjugacy in soluble arithmetic groups
• Sums of two units in number fields
• On the additive and multiplicative structures of the exceptional units in finite commutative rings
• 30 years of collaboration