The Zariski topology for distributive lattices
type: Item
instance of: scholarly article
title: The Zariski topology for distributive lattices
zbMATH Open document ID: 0622.06005
DOI: 10.1216/RMJ-1987-17-2-195
author: Gerhard Gierz
author: Albert R. Stralka
published in: Rocky Mountain Journal of Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The purpose of this paper is to study an intrinsic topology for distributive lattices which by its very definition is analogous to the classical Zariski topology on rings. As in the case of rings, the Zariski topology is the coarsest topology making solution sets of polynomials closed. In other words, the Zariski closed sets are generated from a subbase consisting of all sets of the form \(\{\) \(z\in L:\) \(p(z)=c\}\) where p(x) is a polynomial over L and c is an arbitrary element from L.
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06B30
zbMATH DE Number: 4008458
zbMATH Keywords: topology for distributive lattices
zbMATH Keywords: Zariski closed sets
reviewed by: Richard A. Aló
MaRDI profile type: Publication
full work available at URL: rmj-1987-17-2-195
OpenAlex ID: W2068209182
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description: scientific article; zbMATH DE number 4008458