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 | References | Similar Articles | Additional Information
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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L. V. DiBello, Dedekind fields and some related classes of infinite algebraic number fields, Thesis, University of Rochester, Rochester, N. Y., 1969.
- Warren May, Group algebras over finitely generated rings, J. Algebra 39 (1976), no. 2, 483–511. MR 399232, DOI https://doi.org/10.1016/0021-8693%2876%2990049-1
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Additional Information
Keywords:
Infinite field extension,
abelian field extension cyclotomic field extension,
units
Article copyright:
© Copyright 1970
American Mathematical Society
