Lokalinvariante Bewertungen. (Locally invariant valuations)
type: Item
instance of: scholarly article
title: Lokalinvariante Bewertungen. (Locally invariant valuations)
zbMATH Open document ID: 0578.16007
DOI: 10.1007/BF01179421
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173727
review text: The subject of this paper is locally invariant valuations. These valuations represent a special class of Mathiak's valuations of skew fields. Examples of locally invariant valuations are invariant valuations, subinvariant valuations and valuations of finite dimensional division rings. In the first section, some characterizations of locally invariant valuations are given in terms of their valuation rings and their valuation groups. The second section contains the main result of this paper which concerns the general approximation theorem in the sense of Ribenboim. It is proved, that \(v_ 1,...,v_ n\) satisfy the general approximation theorem, if \(v_ 1,...,v_{n-1}\) are locally invariant. Furthermore, this gives another characterization of locally invariant valuations, since the following holds: a valuation v of K is locally invariant if and only if the general approximation theorem holds for v and an arbitrary valuation w of K.
Mathematics Subject Classification ID: 16Kxx
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 3925025
zbMATH Keywords: Mathiak's valuations of skew fields
zbMATH Keywords: locally invariant valuations
zbMATH Keywords: finite dimensional division rings
zbMATH Keywords: valuation rings
zbMATH Keywords: valuation groups
zbMATH Keywords: approximation theorem
author: Joachim Graeter
MaRDI profile type: Publication
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OpenAlex ID: W4249271099
description: scientific article; zbMATH DE number 3925025