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Proceedings of the American Mathematical Society

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

 

 

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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DOI: https://doi.org/10.1090/S0002-9939-1970-0258786-6
Keywords: Infinite field extension, abelian field extension cyclotomic field extension, units
Article copyright: © Copyright 1970 American Mathematical Society