Maximal ordered fields of rank n
type: Item
instance of: scholarly article
title: Maximal ordered fields of rank n
zbMATH Open document ID: 0627.12016
author: Daiji Kijima
author: Mieo Nishi
published in: Hiroshima Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: An ordered field F has a valuation v compatible with the order, and the rank of this valuation is called the rank of F. We say F is complete if it does not allow of an extension \(\hat F\) in which F is dense. The authors show that any maximal ordered field F of finite rank is complete, where by maximal it is meant one which has no proper ordered extension of the same rank. The main theorem establishes (i) the existence and uniqueness of a maximal ordered field F of rank n for any natural number n, and (ii) any ordered field K of rank n can be order-isomorphically embedded in F. This F is in fact the formal power series field in x with coefficients from R and exponents from the n-fold lexicographic product of the additive group of real numbers \({\mathbb{R}}\).
Mathematics Subject Classification ID: 12J15
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 12D15
zbMATH DE Number: 4019187
zbMATH Keywords: valuation
zbMATH Keywords: maximal ordered field
zbMATH Keywords: formal power series field
reviewed by: N. Sankaran
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4019187