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On Extensions of Valuations with given Residue Field and Value Group

Part of: Field extensions

Published online by Cambridge University Press:  21 December 2009

Figen Öke
Figen Öke
Affiliation:
Trakya University, Department of Mathematics, 22030 Edirne, Turkey, E-mail: [email protected]
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Abstract

Let υ be a valuation on K with value group Gυ, residue field kυ, rank υ = t and K (x1, …, xn) be the field of rational functions over K with n variables. If G is the direct sum of G1 and d infinite cyclic groups where G1 is a totally ordered group containing Gυ as an ordered subgroup with [G1 : Gυ] < ∞ and k′ is a finite field extension of kυ then there exists a residual transcendental extension u of υ to K (x1, …, xn) such that rank u = t + d, Gu = G the algebraic closure of kυ in kυ is k′ and trans deg ku/kυ = n − d.

MSC classification

Secondary: 12F20: Transcendental extensions
Type
Research Article
Information
Mathematika , Volume 55 , Issue 1-2 , December 2009 , pp. 191 - 197
Copyright
Copyright © University College London 2009

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References

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