On distinct unit generated fields that are totally complex

We consider the problem of characterizing all number fields \(K\) such that all algebraic integers \(\alpha\in K\) can be written as the sum of distinct units of \(K\). We extend a method due to Thuswaldner and Ziegler that previously did not work for totally complex fields and apply our results to...

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Bibliographic Details
Published in:arXiv.org 2014-09
Main Authors: Dombek, Daniel, Masáková, Zuzana, Ziegler, Volker
Format: Article
Language:English
Subjects:
Integers
Number theory
Online Access:Get full text
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Summary:We consider the problem of characterizing all number fields \(K\) such that all algebraic integers \(\alpha\in K\) can be written as the sum of distinct units of \(K\). We extend a method due to Thuswaldner and Ziegler that previously did not work for totally complex fields and apply our results to the case of totally complex quartic number fields.
ISSN:2331-8422