A remark on quadratic spaces over noncommutative semilocal rings
type: Item
instance of: scholarly article
title: A remark on quadratic spaces over noncommutative semilocal rings
zbMATH Open document ID: 0653.10021
DOI: 10.1007/BF01183039
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173910
review text: Witt's Cancellation Theorem for quadratic spaces over noncommutative semilocal rings does not hold in general. A ring \(A\) of \(2\times 2\)-matrices and a projective \(A\)-module \(P\) with two nonisomorphic quadratic space structures \(g\) and \(h\) are constructed such that \((P,g)\bot {\mathcal H}(A)\cong (P,h)\bot {\mathcal H}(A)\) (\({\mathcal H}(A)\) the hyperbolic plane). Given the quadratic space \(P\) an upper bound for the number of isometry classes of spaces \(N\) with \(P\bot {\mathcal H}(A)\cong N\bot {\mathcal H}(A)\) is determined.
Mathematics Subject Classification ID: 11E88
Mathematics Subject Classification ID: 16L30
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 4065081
zbMATH Keywords: Witt's Cancellation Theorem
zbMATH Keywords: quadratic spaces
zbMATH Keywords: noncommutative semilocal rings
zbMATH Keywords: upper bound
zbMATH Keywords: number of isometry classes
author: Bernhard Keller
reviewed by: Niels Schwartz
MaRDI profile type: Publication
cites work: Quadratic forms over semilocal rings
cites work: Q3277493
cites work: Isometrien über semilokalen Ringen
cites work: Witt's theorem for noncommutative semilocal rings
cites work: Q3708857
description: scientific article; zbMATH DE number 4065081