Signatures of higher level on rings with many units
type: Item
instance of: scholarly article
title: Signatures of higher level on rings with many units
zbMATH Open document ID: 0676.10016
DOI: 10.1007/BF02570863
author: S. H. Smith
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183760
review text: In this paper, \textit{E. Becker} and \textit{A. Rosenberg}'s theory of higher level reduced forms and reduced Witt rings [J. Algebra 92, 477-503 (1985; Zbl 0555.10009)] is extended to rings with many units, in particular, semi-local rings. Specifically, we show that if A is a ring with many units and \(T\subseteq A\) is a preorder of finite even exponent k then T gives rise to a space of signatures in the sense of \textit{C. Mulcahy} [Commun. Algebra 16, No.3, 577-612 (1988; Zbl 0644.10016)]. A local- global criterion for isotropy and a representation theorem are also obtained, generalizing results of \textit{M. Knebusch} in the case \(k=2\) [Abh. Math. Semin. Univ. Hamb. 51, 149-195 (1981; Zbl 0469.10008)].
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 11E16
Mathematics Subject Classification ID: 13H99
zbMATH DE Number: 4106949
zbMATH Keywords: higher level reduced forms
zbMATH Keywords: reduced Witt rings
zbMATH Keywords: rings with many units
zbMATH Keywords: semi-local rings
zbMATH Keywords: space of signatures
zbMATH Keywords: local-global criterion for isotropy
zbMATH Keywords: representation theorem
MaRDI profile type: Publication
cites work: Quadratic forms over semilocal rings
cites work: Partial orders on a field and valuation rings
cites work: On the description of the reduced Witt ring
cites work: Reduced forms and reduced Witt rings of higher level
cites work: On basic semialgebraic sets
cites work: Sommes de puissances d-ièmes dans un anneau commutatif
cites work: Succinct and representational Witt rings
cites work: On the local theory of signatures and reduced quadratic forms
cites work: An introduction to real algebra
cites work: The Witt Ring of a Space of Ordering
cites work: The Witt ring of a space of signatures
cites work: Projective Modules Over Rings with Many Units
cites work: An abstract approach to higher level forms and rigidity
cites work: Stability index of real varieties
description: scientific article; zbMATH DE number 4106949