On minimal pairs and residually transcendental extensions of valuations

Khanduja, Sudesh K. ; Popescu, N. ; Roggenkamp, K. W. (2002) On minimal pairs and residually transcendental extensions of valuations Mathematika, 49 (1-2). pp. 93-106. ISSN 0025-5793

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1112/S0025579300016090

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 λ̅ of K. It is also shown that these invariants are of independent interest as well. A characterization of those elements a belonging to λ̅ is given such that there exists a minimal pair (a, δ) for some δ in the divisible closure of the value group of v.

Item Type:Article
Source:Copyright of this article belongs to University College London.
Keywords:12J10: Field Theory and Polynomials; Topological Fields; Valued Fields
ID Code:69884
Deposited On:19 Nov 2011 10:25
Last Modified:19 Nov 2011 10:26

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