Free products of pseudocomplemented semilattices
type: Item
instance of: scholarly article
title: Free products of pseudocomplemented semilattices
zbMATH Open document ID: 1005.06002
author: Zuzana Heleyová
author: Tibor Katriňák
published in: Semigroup Forum
publication date: 2000-11-08T00:00:00Z
review text: Let \({\mathcal K}\) be the variety of pseudocomplemented semilattices (PCSs in brief), let \(S\), \(S_i\in{\mathcal K}\), for \(i\in I\). Then \(S\) is a free product of \(S_i\) \((i\in I)\) if there exist embeddings \(\varphi_i: S_i\to S\) such that \(S\) is generated by the set \(\bigcup \{\varphi_i(S_i);\;i\in I\}\), and if \(T\in K\) and \(\psi_i:S_i\to T\) are homomorphisms then there exists a homomorphism \(\psi:S\to T\) such that \(\psi_i=\varphi_i \circ\psi\). It is the aim of the paper to provide a characterization of the free products of PCSs. To this end the authors exploit known results on free products of Boolean algebras. Moreover, they derive an alternative description of the free PCSs.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06D15
Mathematics Subject Classification ID: 06E05
zbMATH DE Number: 1445563
zbMATH Keywords: free pseudocomplemented semilattice
zbMATH Keywords: free products
zbMATH Keywords: Boolean algebras
MaRDI profile type: Publication
full work available at URL: s002339910037
OpenAlex ID: W2038055266
DOI: 10.1007/S002339910037
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description: scientific article; zbMATH DE number 1445563