<div class="csl-bib-body">
<div class="csl-entry">Cenker, V., Chajda, I., & Länger, H. (2025, September 11). <i>Properties of the symmetric difference in lattices with complementation</i> [Conference Presentation]. Summer School on General Algebra and Ordered Sets 2025, Blansko, Czechia. http://hdl.handle.net/20.500.12708/219504</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/219504
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dc.description.abstract
The symmetric difference in Boolean lattices can be defined in two different but equivalent forms. However, it can be introduced also in every bounded lattice with complementation where these two forms need not coincide. We study lattices with complementation where these two expressions coincide. It is well-known that the symmetric difference is associative in every Boolean lattice. We prove that this is just the property of Boolean lattices, namely the symmetric difference in a lattice with complementation is associative if and only if this lattice is Boolean. Similarly, we prove that a lattice with complementation is Boolean if and only if the symmetric difference satisfies a certain simple identity in two variables.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.subject
complemented lattice
en
dc.subject
lattice with complementation
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dc.subject
symmetric difference
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dc.subject
De Morgan's laws
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dc.subject
distributivity
en
dc.subject
associativity
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dc.subject
variety of lattices with complementation
en
dc.subject
free algebra
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dc.title
Properties of the symmetric difference in lattices with complementation
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.contributor.affiliation
Palacký University Olomouc, Czechia
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dc.contributor.affiliation
Algebra and Geometry - Palacky University, Faculty of Sciences (OLOMOUC, CZ)
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dc.relation.grantno
PIN5424624
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dc.type.category
Conference Presentation
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tuw.project.title
Orthogonalität und Symmetrie
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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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tuw.publication.orgunit
E104-01 - Forschungsbereich Algebra
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tuw.author.orcid
0000-0003-3840-3879
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tuw.event.name
Summer School on General Algebra and Ordered Sets 2025
en
dc.description.sponsorshipexternal
Czech Science Foundation
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dc.description.sponsorshipexternal
IGA
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dc.description.sponsorshipexternal
Czech Science Foundation
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dc.relation.grantnoexternal
24-14386L
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dc.relation.grantnoexternal
PrF 2025 008
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dc.relation.grantnoexternal
25-20013L
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tuw.event.startdate
07-09-2025
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tuw.event.enddate
12-09-2025
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Blansko
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tuw.event.country
CZ
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tuw.event.presenter
Länger, Helmut
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.grantfulltext
none
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item.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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item.cerifentitytype
Publications
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item.fulltext
no Fulltext
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crisitem.project.funder
FWF - Österr. Wissenschaftsfonds
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crisitem.project.grantno
PIN5424624
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crisitem.author.dept
Palacký University Olomouc, Czechia
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crisitem.author.dept
Algebra and Geometry - Palacky University, Faculty of Sciences (OLOMOUC, CZ)
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crisitem.author.dept
E104 - Institut für Diskrete Mathematik und Geometrie
