On rings of integers generated by their units

Details On rings of integers generated by their units On rings of integers generated by their units

2010-09-02

arxiv.org/abs/1009.0447v3

Bull. London Math. Soc. 44: 167-182, 2012

Mathematics

Number Theory

15 pages

Scientific paper

10.1112/blms/bdr089

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.

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