Bimodule-valued hermitian and quadratic forms
type: Item
instance of: scholarly article
title: Bimodule-valued hermitian and quadratic forms
zbMATH Open document ID: 0823.11015
DOI: 10.1007/BF01198668
author: Ottmar Loos
published in: Archiv der Mathematik
publication date: 1995-04-18T00:00:00Z
review text: Let \(k\) be a commutative ring and \(A\) a unital associative \(k\)-algebra. The author introduces the notion of a hermitian form with values in a \((A\)-\(A^{op})\)-bimodule \(L\). The notion of a form parameter, as introduced by Bak, appears as the special case where \(L\) is an invertible \((A\)-\(A^{op})\)-bimodule which is free on one generator as a right \(A\)- module. The main result is that \(L\)-valued forms, with \(L\) invertible, occur naturally in the categorical setting of \textit{H. Quebbemann}, \textit{W. Scharlau} and \textit{M. Schulte} [J. Algebra 59, 264-289 (1979; Zbl 0412.18016)]. They are the hermitian and quadratic forms (in this categorical setting) on the category of finitely generated projective \(A\)-modules.
reviewed by: M.-A. Knus
Mathematics Subject Classification ID: 11E39
Mathematics Subject Classification ID: 11E81
zbMATH DE Number: 743515
zbMATH Keywords: bimodule-valued forms
zbMATH Keywords: projective modules
zbMATH Keywords: hermitian form
zbMATH Keywords: form parameter
zbMATH Keywords: quadratic forms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 743515