Free pseudocomplemented semilattices: a new approach.
type: Item
instance of: scholarly article
title: Free pseudocomplemented semilattices: a new approach.
zbMATH Open document ID: 1326.06008
author: J. Guričan
author: Tibor Katriňák
published in: Algebra Universalis
publication date: 2015-10-14T00:00:00Z
review text: The concept of a plain pseudocomplemented semilattice is introduced. It is shown that every plain pseudocomplemented semilattice \(S\) is sectionally pseudocomplemented and the canonical form for elements from \(S\) is derived. It is proved that every free pseudocomplemented semilattice is plain. A necessary and sufficient condition for a pseudocomplemented semilattice to be freely generated by a set \(X\) is presented (the main result). If \(F\) is a free pseudocomplemented semilattice then \(B(F)\) is a free Boolean algebra.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06D15
Mathematics Subject Classification ID: 08B20
zbMATH DE Number: 6494313
zbMATH Keywords: free pseudocomplemented semilattices
zbMATH Keywords: sectionally pseudocomplemented semilattices
zbMATH Keywords: free PCS
zbMATH Keywords: plain pseudocomplemented semilattices
MaRDI profile type: Publication
full work available at URL: s00012-015-0345-0
OpenAlex ID: W1682037263
cites work: Free products of pseudocomplemented semilattices -- revisited
cites work: On free pseudo-complemented and relatively pseudo-complemented semi-lattices
cites work: Q4083730
cites work: Q5532570
cites work: Q4138766
cites work: Pseudo-complemented modular semilattices
cites work: Pseudo-complements in semi-lattices
cites work: Lattice Theory: Foundation
cites work: The category of semilattices
cites work: Q4126563
cites work: Finite pseudocomplemented lattices: The spectra and the Glivenko congruence
cites work: Projective pseudo complemented semilattices
cites work: Die Kennzeichnung der distributiven pseudokomplementären Halbverbände.
cites work: Free p-algebras
cites work: Q3574507
cites work: Free products of pseudocomplemented semilattices
cites work: Implicative Semi-Lattices
cites work: Q5752619
DOI: 10.1007/S00012-015-0345-0
description: scientific article; zbMATH DE number 6494313