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Zbl 0774.12009
Popescu, Nicolae; Vraciu, Constantin
On the extension of valuations on a field $K$ to $K(X)$. I. (English)
[J] Rend. Semin. Mat. Univ. Padova 87, 151-168 (1992). ISSN 0041-8994

The theme of this paper is to give a description of the extensions of all valuations of a field $K$ to the field of rational functions $K(X)$ in one variable $X$, and to classify them. For this, the authors introduce and give examples of quasi unramified extensions, residual transcendental extensions and show that any residual transcendental extension is quasi unramified. Theorem 3.3 gives a connection between extension of a valuation and valuation induced on the residue field. In the last section, the extensions of a valuation of an algebraically closed field $K$ to $K(X)$ are classified as being of two kinds (the first and second kind and a description of the second kind is given).
[N.Sankaran (Chandigarh)]

MSC 2000:: *12J20 General valuation theory
12F99 Field extensions

Keywords: extension of valuations; field of rational functions; quasi unramified extensions; residual transcendental extensions

Cited in: Zbl 0881.12004

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