Unit groups of infinite abelian extensions
Abstract: Let be a finite extension field of the rational numbers, , and let be an infinite abelian extension of . Let be a finite set of prime divisors of including the Archimedean one. An -unit of is a field element which is a local unit at all prime divisors of which do not restrict on to a member of . It is shown that the group of -units of is the direct product of the group of roots of unity of 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