<div class="csl-bib-body">
<div class="csl-entry">Chajda, I., Kolařík, M., & Länger, H. (2025). Induced orthogonality in semilattices with 0 and in pseudocomplemented lattices and posets. <i>ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS</i>, <i>42</i>(3), 577–592. https://doi.org/10.1007/s11083-025-09696-y</div>
</div>
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dc.identifier.issn
0167-8094
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/221298
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dc.description.abstract
On an arbitrary meet-semilattice S = (S, ∧, 0) with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if S is atomic then Cl(S)is a complete atomic Boolean algebra. If S is a pseudocomplemented lattice, this orthogonality relation can be defined by means of the pseudocomplementation. Finally, we show that if S is a complete pseudocomplemented lattice then Cl(S) is a complete Boolean algebra. For pseudocomplemented posets a similar result holds if the subset of pseudocomplements forms a complete lattice satisfying a certain compatibility condition.
en
dc.language.iso
en
-
dc.publisher
SPRINGER
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dc.relation.ispartof
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
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dc.subject
meet-semilattice
en
dc.subject
lattice
en
dc.subject
orthogonality
en
dc.subject
closed subset
en
dc.subject
ortholattice
en
dc.subject
Boolean algebra
en
dc.subject
pseudocomplemented lattice
en
dc.subject
pseudocomplemented poset
en
dc.title
Induced orthogonality in semilattices with 0 and in pseudocomplemented lattices and posets
en
dc.type
Article
en
dc.type
Artikel
de
dc.contributor.affiliation
Palacký University Olomouc, Czechia
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dc.contributor.affiliation
Palacký University Olomouc, Czechia
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dc.description.startpage
577
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dc.description.endpage
592
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dc.type.category
Original Research Article
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tuw.container.volume
42
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tuw.container.issue
3
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tuw.journal.peerreviewed
true
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tuw.peerreviewed
true
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wb.publication.intCoWork
International Co-publication
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tuw.researchTopic.id
X1
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tuw.researchTopic.name
Beyond TUW-research focus
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tuw.researchTopic.value
100
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dcterms.isPartOf.title
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
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tuw.publication.orgunit
E104-01 - Forschungsbereich Algebra
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tuw.publisher.doi
10.1007/s11083-025-09696-y
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dc.date.onlinefirst
2025-01-25
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dc.identifier.eissn
1572-9273
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dc.description.numberOfPages
16
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tuw.author.orcid
0000-0003-3840-3879
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dc.description.sponsorshipexternal
Czech Science Foundation
-
dc.description.sponsorshipexternal
IGA
-
dc.relation.grantnoexternal
24-14386L
-
dc.relation.grantnoexternal
PrF 2025 008
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wb.sci
true
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wb.sciencebranch
Informatik
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1020
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
5
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wb.sciencebranch.value
95
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item.openairecristype
http://purl.org/coar/resource_type/c_2df8fbb1
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Publications
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item.openairetype
research article
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item.languageiso639-1
en
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restricted
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no Fulltext
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crisitem.author.dept
Algebra and Geometry - Palacky University, Faculty of Sciences (OLOMOUC, CZ)
-
crisitem.author.dept
Palacký University Olomouc
-
crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie