Lokalinvariante Bewertungen. (Locally invariant valuations)
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.
scientific article; zbMATH DE number 3925025