Quadratic and \(\lambda\)-Hermitian forms
type: Item
instance of: scholarly article
title: Quadratic and \(\lambda\)-Hermitian forms
zbMATH Open document ID: 0688.10022
DOI: 10.1016/0022-4049(89)90118-7
author: Michel Carral
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: The author gives algebro-topological conditions for a unitary subring A of a topological ring B to have, up to isomorphism, the same quadratic or \(\lambda\)-Hermitian forms as B. These conditions are formulated for a topological ring R in terms of the topology of R, together with an involution, and an element, \(\lambda\), in the center of R. For \(\lambda =1\) and the trivial involution, the above condition has been used by \textit{R. G. Swan} [Trans. Am. Math. Soc. 230, 201-234 (1977; Zbl 0443.13005)] in the study of the relationship between isomorphism classes of finitely generated projective modules over A and over B, respectively. The examples in the paper concern the ring C(X,k) of continuous k-valued functions on a topological space X \((k={\mathbb{R}}\), \({\mathbb{C}}\) or \({\mathbb{H}})\). In the reviewer's opinion the author should have indicated the topology that he considered in these rings, because in cases where X is not compact there are several choices.
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 13J99
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 4127309
zbMATH Keywords: quadratic forms
zbMATH Keywords: topological ring
zbMATH Keywords: \(\lambda\)-Hermitian forms
reviewed by: Enrique Outerelo
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90118-7
OpenAlex ID: W2085699381
cites work: Q4053793
cites work: Witt rings and K-theory
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description: scientific article; zbMATH DE number 4127309