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An Approximation Theorem for Extended Prime Spots

Published online by Cambridge University Press:  20 November 2018

Ron Brown
Ron Brown*
Affiliation:
University of Oregon, Eugene, Oregon; Simon Fraser University, Burnaby, British Columbia
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We introduce here a generalization to arbitrary fields of the prime spots of algebraic number theory, essentially by allowing absolute values to take the value ∞. The set of “extended” prime spots of a field admits a natural topology, and an approximation theorem is given here for compact sets of extended prime spots. Among the corollaries of the approximation theorem are the weak approximation theorem for absolute values [13, p. 8], Ribenboim's generalization of the approximation theorem for independent valuations [14, p. 136], Stone's approximation theorem for type V topologies [16, p. 20], and an approximation theorem for Harrison primes.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 1 , February 1972 , pp. 167 - 184
Copyright
Copyright © Canadian Mathematical Society 1972

References

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