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

Khanduja, Sudesh K. (1991) Prolongations of valuations to simple transcendental extensions with given residue field and value group Mathematika, 38 (02). pp. 386-390. ISSN 0025-5793

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Related URL: http://dx.doi.org/10.1112/S0025579300006732

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 G0⊆G1⊆G 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).

Item Type:Article
Source:Copyright of this article belongs to University College London.
Keywords:12f20: Field Theory and Polynomial; Field Extensions; Transcendental Extensions
ID Code:69900
Deposited On:17 Nov 2011 03:37
Last Modified:17 Nov 2011 03:37

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