Some examples of valued fields
type: Item
instance of: scholarly article
title: Some examples of valued fields
zbMATH Open document ID: 0846.12005
published in: Journal of Algebra
publication date: 1996-10-07T00:00:00Z
review text: The author uses a generalized power series \(A= [[ R^{S,\leq} ]]\) to provide two classes of examples of valued fields, where \(A\) is the set of all mappings \(f: S\to R\) (\(S\) is a torsion-free abelian group with a compatible partial order \(\leq\)) with artinian and narrow support. A lot of results were proved by the author in [Manuscr. Math. 75, 115-150 (1992; Zbl 0767.12001)] which are of the following character: If the field \(R\) has a property \((P)\) and a torsion-free subtotally ordered group \((S, \leq)\) has a property \((Q)\), then \(A\) has also the property \((P)\). In this paper in the first set of examples the valued fields are henselian in general not maximal, with given residue field and value group and in the second set of examples, the valued fields are all maximal and their families of residue fields and value groups form chains. Some additional properties of these examples are investigated.
reviewed by: Jiří Močkoř
Mathematics Subject Classification ID: 12J10
zbMATH DE Number: 763966
zbMATH Keywords: generalized power series
zbMATH Keywords: valued fields
author: Paulo Ribenboim
MaRDI profile type: Publication
full work available at URL: jabr.1995.1108
OpenAlex ID: W2068395291
DOI: 10.1006/JABR.1995.1108
description: scientific article; zbMATH DE number 763966