Posets generated by irreducible elements
type: Item
instance of: scholarly article
title: Posets generated by irreducible elements
zbMATH Open document ID: 1039.06001
DOI: 10.1023/A:1024438130716
author: Branimir Šešelja
author: Andreja Tepavčević
author: Marcel Erné
published in: Order
publication date: 2003-08-21T00:00:00Z
review text: Let \(J\) be a poset and \(L\) the Alexandroff completion of \(J\). Let be \(C_0L= \{P: J\subseteq P\subseteq L\), \(J(P)= J\}\) where \(J(P)\) is the set of all \(\vee\)-irreducible elements of \(P\). The complete lattices in \(C_0L\) form a closure system \(C_\infty L\). The posets for which \(C_0L\) is a complete Boolean atomic lattice and posets for which \(C_\infty L\) is distributive (or modular) are described. Similar results for \(C_k L\), the closure system of all posets in \(C_0 L\) that are closed under meets of less than \(k\) elements (\(k\) a cardinal number), are obtained.
reviewed by: Václav Slaví k
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06B23
zbMATH DE Number: 1968904
zbMATH Keywords: complete lattice
zbMATH Keywords: completion
zbMATH Keywords: irreducibility
zbMATH Keywords: join-dense poset
MaRDI profile type: Publication
full work available at URL: a:1024438130716
OpenAlex ID: W2290451660
description: scientific article; zbMATH DE number 1968904