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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Unit groups of infinite abelian extensions


Author: Warren May
Journal: Proc. Amer. Math. Soc. 25 (1970), 680-683
MSC: Primary 10.65
DOI: https://doi.org/10.1090/S0002-9939-1970-0258786-6
MathSciNet review: 0258786
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Abstract: Let $F$ be a finite extension field of the rational numbers, $Q$, and let $K$ be an infinite abelian extension of $F$. Let $S$ be a finite set of prime divisors of $Q$ including the Archimedean one. An $S$-unit of $K$ is a field element which is a local unit at all prime divisors of $F$ which do not restrict on $Q$ to a member of $S$. It is shown that the group of $S$-units of $K$ is the direct product of the group of roots of unity of $K$ with a free abelian group.


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Keywords: Infinite field extension, abelian field extension cyclotomic field extension, units
Article copyright: © Copyright 1970 American Mathematical Society