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On minimal pairs and residually transcendental extensions of valuations

Part of: Topological fields

Published online by Cambridge University Press:  26 February 2010

Sudesh K. Khanduja ,
N. Popescu  and
K. W. Roggenkamp
Sudesh K. Khanduja
Affiliation:
Departmcnt of Mathematics, Punjab University. Chandigarh-160014. India. E-mail:skhand@pu.ae.in
N. Popescu
Affiliation:
Institute of Mathematics of the Romanian, Academy, P.O. Box 1-764, Bucharest 70700, Romania. E-mail:Nicolae.Popescu@imar.ro
K. W. Roggenkamp
Affiliation:
Mathcmatisches Institut B, Universitat Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany. E-mail:roggenkamp@mathematik.uni-stuttgart.de
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Abstract

In this paper, further insight is obtained into the earlier approach of studying residually transcendental extensions of a valuation v of a field K to a simple transcendental extension K(x) of K by means of minimal pairs, thereby introducing new invariants corresponding to any element of an algebraic closure of K. It is also shown that these invariants are of independent interest as well. A characterization of those elements a belonging to is given such that there exists a minimal pair (a, δ) for some δ in the divisible closure of the value group of v.

MSC classification

Secondary: 12J10: Valued fields
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 93 - 106
Copyright
Copyright © University College London 2002

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