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Hilbertianity of fields of power series

Part of: General field theory

Published online by Cambridge University Press:  13 December 2011

Elad Paran
Elad Paran
Affiliation:
Einstein Institute of Mathematics, J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (paranela@post.tau.ac.il)
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Abstract

Let R be a domain contained in a rank-1 valuation ring of its quotient field. Let R⟦X⟧ be the ring of formal power series over R, and let F be the quotient field of R⟦X⟧. We prove that F is Hilbertian. This resolves and generalizes an open problem of Jarden, and allows to generalize previous Galois-theoretic results over fields of power series.

Keywords

Hilbertian fieldsformal power seriesfield arithmeticgeneralized Krull domains

MSC classification

Secondary: 12E30: Field arithmetic
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 2 , April 2012 , pp. 351 - 361
Copyright
Copyright © Cambridge University Press 2012

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