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arXiv:1009.0447 [math.NT]AbstractReferencesReviewsResources

On rings of integers generated by their units

Christopher Frei

Published 2010-09-02, updated 2012-04-02Version 3

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.

Comments: 15 pages
Journal: Bull. London Math. Soc. 44: 167-182, 2012
Categories: math.NT
Subjects: 11R04, 11R27
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