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Hilbertianity of fields of power series
Published online by Cambridge University Press: 13 December 2011
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.
MSC classification
- 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