Characterizing reduced Witt rings of higher level
type: Item
instance of: scholarly article
title: Characterizing reduced Witt rings of higher level
zbMATH Open document ID: 0587.10011
author: Victoria Powers
published in: Pacific Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Mulcahy's spaces of signatures (SOS) is an abstract setting for the reduced Witt rings of higher level of Becker and Rosenberg just as Marshall's spaces of orderings is an abstract setting for the ordinary reduced Witt ring. Finitely constructable SOS's are those built up in a finite number of steps from the smallest SOS using two operations. We show that finitely constructable SOS's are precisely those that arise from preordered fields (subject to a certain finiteness condition). This allows us to give an inductive construction for the reduced Witt rings of higher level for certain preordered fields, which generalizes a result of Craven for the ordinary reduced Witt ring. We also obtain a generalization of Bröcker's results on the possible number of orderings of a field.
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 11E76
zbMATH DE Number: 3941618
zbMATH Keywords: spaces of signatures
zbMATH Keywords: reduced Witt rings of higher level
zbMATH Keywords: preordered fields
zbMATH Keywords: higher level ordering
MaRDI profile type: Publication
full work available at URL: pjm.1987.128.333
OpenAlex ID: W2087768720
DOI: 10.2140/PJM.1987.128.333
description: scientific article; zbMATH DE number 3941618