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September 2011 Units in real cyclic fields
Roman Marszałek
Funct. Approx. Comment. Math. 45(1): 139-153 (September 2011). DOI: 10.7169/facm/1317045238

Abstract

Let $N/\mathbb{Q}$ be a real cyclic and tame extension of prime degree $l$ with $\Gamma=\mathscr{G}al(N/\mathbb{Q})$. We give the Hom description of the class of the torsion-free part of the group of units in $N$ in the class group of the order $\mathbb{Z}\Gamma/ (\sum_{\gamma \in \Gamma}\gamma )$. This representation depends only on the structure of the ideal class group of $N$ and determines the Galois module structure of the torsion-free part of the group of units in $N$ as an ideal of the $l$th cyclotomic field. Using this approach we derive necessary and sufficient conditions for all real and tame cyclic fields of prime degree to have Minkowski units. We extend also the class of known cyclic real fields with Minkowski units.

Citation

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Roman Marszałek. "Units in real cyclic fields." Funct. Approx. Comment. Math. 45 (1) 139 - 153, September 2011. https://doi.org/10.7169/facm/1317045238

Information

Published: September 2011
First available in Project Euclid: 26 September 2011

zbMATH: 1258.11093
MathSciNet: MR2865419
Digital Object Identifier: 10.7169/facm/1317045238

Subjects:
Primary: 11R33
Secondary: 11S40

Rights: Copyright © 2011 Adam Mickiewicz University

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Vol.45 • No. 1 • September 2011
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