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Prolongations of valuations to simple transcendental extensions with given residue field and value group

Part of: Field extensions

Published online by Cambridge University Press:  26 February 2010

Sudesh K. Khanduja
Sudesh K. Khanduja
Affiliation:
Dr. S. K. Khanduja, Centre for Advanced Study in Mathematics, Panjab University, Chandigarh–160014, India.
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Abstract

Let K0(x) be a simple transcendental extension of a field K0, υ0 be a valuation of K0 with value group G0 and residue field K0. Suppose is an inclusion of totally ordered abelian groups with [G1: G0] < ∞ such that G is the direct sum of G1 and an infinite cyclic group. It is proved that there exists an (explicitly constructible) valuation υ of K0(x) extending υ0 such that the value group of υ is G and its residue field is k, where k is a given finite extension of k0. This is analogous to a result of Matignon and Ohm [2, Corollary 3.2] for residually non-algebraic prolongations of υ0 to K0(x).

MSC classification

Secondary: 12F20: Transcendental extensions
Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 386 - 390
Copyright
Copyright © University College London 1991

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References

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