Topological characterization of certain classes of lattices
type: Item
instance of: scholarly article
title: Topological characterization of certain classes of lattices
zbMATH Open document ID: 0709.06005
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108171
review text: Let L be a distributive lattice with 0 and 1, and let Spec L be the set of all proper prime ideals of L. Spec L can be endowed with two topologies, the spectral topology and the D-topology. It is proved that there is a bijection from the set of all \(\sigma\)-ideals of L to the set of all D-open subsets of Spec L. Let Max L and Min L be the sets of maximal ideals and minimal prime ideals of L, respectively. The author proves that the two topologies coincide on Spec L, Max L and Min L, if and only if L is a Boolean, Stonian, and normal lattice, respectively.
reviewed by: S.Gacsályi
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06B30
zbMATH DE Number: 4164926
zbMATH Keywords: distributive lattice
zbMATH Keywords: prime ideals
zbMATH Keywords: spectral topology
zbMATH Keywords: D-topology
author: H. Al-Ezeh
MaRDI profile type: Publication
cites work: Q5574727
cites work: Normal lattices
cites work: Projectivity of pure ideals
cites work: Isomorphic sheaf representations of normal lattices
cites work: Q3965241
cites work: Disconnexités des spectres d'anneaux et des préschémas
cites work: Reticulated rings
cites work: Some Remarks on a Class of Distributive Lattices
description: scientific article; zbMATH DE number 4164926