Structure sheaves and noncommutative topologies
type: Item
instance of: scholarly article
title: Structure sheaves and noncommutative topologies
zbMATH Open document ID: 0882.16018
author: M. García
published in: Journal of Algebra
publication date: 1997-10-01T00:00:00Z
full work available at URL: 5122.pdf
review text: The main purpose of this paper is to construct structure sheaves over noncommutative topologies associated to an arbitrary left noetherian ring. In the first section the authors quickly recollect some of the main notions, constructions and results, which will be needed throughout. In the second section, they study localization at elements in the free semigroup generated by all Gabriel filters over a fixed base ring and prove its main properties. In particular, they show how the main results of \textit{A. Verschoren} [J. Algebra 182, No. 2, 341-346 (1996; Zbl 0863.16024)] may be generalized to this set-up. In the last section, they introduce noncommutative topologies over an arbitrary ring and show how the former results may be applied to construct structure sheaves over these. Some examples are included, showing their methods to generalize previous sheaf constructions in the literature.
Mathematics Subject Classification ID: 16S60
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 1053882
zbMATH Keywords: structure sheaves
zbMATH Keywords: noncommutative topologies
zbMATH Keywords: left Noetherian rings
zbMATH Keywords: localizations
zbMATH Keywords: Gabriel filters
reviewed by: Yoshiki Kurata
MaRDI profile type: Publication
OpenAlex ID: W1976214609
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DOI: 10.1006/JABR.1996.7004
description: scientific article; zbMATH DE number 1053882