The real spectrum of a noncommutative ring
type: Item
instance of: scholarly article
title: The real spectrum of a noncommutative ring
zbMATH Open document ID: 0909.16027
author: Ka Hin Leung
author: Murray Marshall
author: Yu-Fei Zhang
published in: Journal of Algebra
publication date: 1999-04-07T00:00:00Z
review text: Orderings on commutative rings have been studied extensively in the context of real algebraic geometry and, in particular, the study of semi-algebraic sets, since the early work by Coste and Roy (in the early 80s) on the real spectrum. In particular, it is now well-known that orderings on a real commutative ring yield an abstract real spectrum (or space of signs), in the sense of Bröckner et al. This is basically due to the fact that, on the one hand, the axioms defining real spectra generalize those for spaces of orderings, while on the other the residue space \((X_p,G_p)\) at any prime \(p\) of an abstract real spectrum \((X,G)\) is a space of orderings. The main purpose of the present paper is to take a look at what happens in the noncommutative case. The surprising, main result in the present paper is that it may be shown that orderings of noncommutative rings give rise to abstract real spectra, just as in the commutative case.
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 14A22
Mathematics Subject Classification ID: 14P10
zbMATH DE Number: 1106617
zbMATH Keywords: semi-algebraic sets
zbMATH Keywords: real spectra
zbMATH Keywords: spaces of orderings
zbMATH Keywords: orderings of noncommutative rings
MaRDI profile type: Publication
OpenAlex ID: W2071737187
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DOI: 10.1006/JABR.1997.7145
description: scientific article; zbMATH DE number 1106617