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Zbl 0923.12010
Alexandru, V.; Popescu, A.; Popescu, N.
Completion of r. t. extensions of local fields. II. (English)
[J] Rend. Semin. Mat. Univ. Padova 100, 57-66 (1998). ISSN 0041-8994

Let $(K,v)$ be a local field. An extension $w$ of $v$ to $K(X)$ is called residual transcendental (r.t.-extension) if the residue field of $w$ is a transcendental extension of the residual field of $v$. In the first part of this paper [Math. Z. 221, 675-682 (1996; Zbl 0852.12003)] the authors described the completion $(\widetilde{K(X)},\widetilde w)$ of $(K(X),w) $, where $w$ is the Gauss r.t.-extension of $v$. In this paper they consider the general case of any r.t.-extension of $v$. For the description of elements of the completion they use the embedding of $(K(X),w)$ into the valued field $K' \{\{X-a.\delta\}\}$ of $\delta$-formal Laurent series over the local field $(K', v')$, where $\delta$ is an appropriate rational number, and $K'=K(a) \subset \overline K$, $a\in\overline K$ (the algebraic closure of $K)$. Moreover, they describe $(\widetilde{K(X)},\widetilde w)$ as a finite extension of $(\widetilde {K(r)}, \widetilde{w_0})$, where $r\in K(X)$ and $w_0$ is the Gauss r.t.-extension of $v$.
[J.Močkoř (Ostrava)]

MSC 2000:: *12J10 Valued fields
12F99 Field extensions
12J20 General valuation theory

Keywords: residual transcendental extension; local field

Citations: Zbl 0852.12003

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