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On minimal pairs and residually transcendental extensions of valuations
- Source :
- Mathematika. 49:93-106
- Publication Year :
- 2002
- Publisher :
- Wiley, 2002.
-
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 λ of K. It is also shown that these invariants are of independent interest as well. A characterization of those elements a belonging to λ is given such that there exists a minimal pair (a, δ) for some δ in the divisible closure of the value group of v.
Details
- ISSN :
- 20417942 and 00255793
- Volume :
- 49
- Database :
- OpenAIRE
- Journal :
- Mathematika
- Accession number :
- edsair.doi...........e9755664eec61937d8deb828850331a3