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Arithmetic on Groups of Positive Rationals

✍ Scribed by Clifford S. Queen

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
123 KB
Volume
92
Category
Article
ISSN
0022-314X

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✦ Synopsis

In this paper we develop a theory of unique factorization for subgroups of the positive rationals. We show that this theory is strong enough to include arithmetic progressions and the theory of genera in algebraic number fields. We establish generalizations of both Dirichlet's theorem on primes in arithmetic progressions and the theory of genera for Abelian extensions of the rationals.

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