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On Dirichlet's theorem and infinite primes


Author: Carter Waid
Journal: Proc. Amer. Math. Soc. 44 (1974), 9-11
MSC: Primary 10N15; Secondary 02H25
DOI: https://doi.org/10.1090/S0002-9939-1974-0335466-3
MathSciNet review: 0335466
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Abstract: It is shown that Dirichlet's theorem on primes in an arithmetic progression is equivalent to the statement that every unit of a certain quotient ring $ \bar Z$ of the nonstandard integers is the image of an infinite prime. The ring $ \bar Z$ is the completion of $ Z$ relative to the ``natural'' topology on $ Z$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0335466-3
Keywords: Dirichlet's theorem, nonstandard arithmetic, infinite primes, units, completions
Article copyright: © Copyright 1974 American Mathematical Society