Witt's theorems for Galois ring valued quadratic forms
type: Item
instance of: scholarly article
title: Witt's theorems for Galois ring valued quadratic forms
zbMATH Open document ID: 1155.11021
published in: Journal of Pure and Applied Algebra
publication date: 2008-09-04T00:00:00Z
review text: A Galois ring of \(q^2\) elements, where \(q=2^\ell\), is a local ring \(R\) with maximal ideal \(2R\) and residue class field \(R/2R=\text{ GF}(q)\). Quadratic forms with values in a Galois ring were studied by \textit{J. A. Wood} [Trans. Am. Math. Soc. 336, No. 1, 445--461 (1993; Zbl 0766.15033)] and the authors [Finite Fields Appl. 13, No. 4, 946--961 (2007; Zbl 1137.11024)]. Here the authors prove the Witt cancellation and the Witt extension theorems for Galois ring valued quadratic forms.
Mathematics Subject Classification ID: 11E08
Mathematics Subject Classification ID: 13M99
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 5321423
zbMATH Keywords: Galois ring valued quadratic forms
zbMATH Keywords: Witt cancellation theorem
zbMATH Keywords: Witt extension theorem
zbMATH Keywords: Clifford algebras
author: María Concepción López-Díaz
author: Ignacio F. Rua
reviewed by: Kazimierz Szymiczek
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.03.028
OpenAlex ID: W2062409597
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DOI: 10.1016/J.JPAA.2008.03.028
description: scientific article; zbMATH DE number 5321423