Record link: 
http://hdl.handle.net/20.500.12708/221298
-
Title: 
Induced orthogonality in semilattices with 0 and in pseudocomplemented lattices and posets
en
Citation: 
Chajda, I., Kolařík, M., & Länger, H. (2025). Induced orthogonality in semilattices with 0 and in pseudocomplemented lattices and posets. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 42(3), 577–592. https://doi.org/10.1007/s11083-025-09696-y
-
Publisher DOI: 
10.1007/s11083-025-09696-y
-
Publication Type: 
Article - Original Research Article
en
Language: 
English
-
Authors: 
Chajda, Ivan 
Kolařík, Miroslav 
Länger, Helmut 
-
Organisational Unit: 
E104-01 - Forschungsbereich Algebra 
-
Journal: 
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS 
-
ISSN: 
0167-8094
-
Date (published): 
2025
-
Number of Pages: 
16
-
Publisher: 
SPRINGER
-
Peer reviewed: 
Yes
-
Keywords: 
meet-semilattice; lattice; orthogonality; closed subset; ortholattice; Boolean algebra; pseudocomplemented lattice; pseudocomplemented poset
en
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
Project (external): 
Czech Science Foundation
IGA
-
Project ID: 
24-14386L
PrF 2025 008
-
Research Areas: 
Beyond TUW-research focus: 100%
-
Science Branch: 
1020 - Informatik: 5%
1010 - Mathematik: 95%
-
Appears in Collections:
Article

Show full item record

Google ScholarTM

Check