Arithmetic on Groups of Positive Rationals |
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Authors: | Clifford S. Queen |
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Affiliation: | Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania, 18015 |
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Abstract: | 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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