Round quadratic forms under algebraic extensions
type: Item
instance of: scholarly article
title: Round quadratic forms under algebraic extensions
zbMATH Open document ID: 0671.10016
author: Burkhard Alpers
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Pfister forms over fields are those anisotropic forms that remain round under any field extension. Here, round means that for any non-zero represented element x the isometry \(q\cong xq\) holds where q is the form under consideration. We investigate whether a similar characterization can be given for the round forms themselves. We get several ``going-up''- and ``going-down''-theorems. Some counter-examples are given which show that neither in the ``going-up'' nor in the ``going-down'' situation a general theorem holds.
reviewed by: Burkhard Alpers
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 12F99
Mathematics Subject Classification ID: 11E81
Mathematics Subject Classification ID: 12D15
zbMATH DE Number: 4097473
zbMATH Keywords: quadratic forms
zbMATH Keywords: round forms
zbMATH Keywords: going-up
zbMATH Keywords: going-down
zbMATH Keywords: birigid elements
zbMATH Keywords: non-formally real fields
MaRDI profile type: Publication
full work available at URL: pjm.1991.147.213
OpenAlex ID: W2088984255
DOI: 10.2140/PJM.1991.147.213
description: scientific article; zbMATH DE number 4097473