On Dirichlet’s theorem and infinite primes
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- by Carter Waid PDF
- Proc. Amer. Math. Soc. 44 (1974), 9-11 Request permission
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
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Additional Information
- © Copyright 1974 American Mathematical Society
- 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