Zdenka
Riečanová
133-141
base poset
2022-01-01T18:05
orthoposets
category of orthoalgebras
finite chains
examples of posets
lattice
difference orthoalgebraic structure
complete lattice
difference orthoposets
completion
difference operation
false
https://scigraph.springernature.com/explorer/license/
categories
orthoalgebraic structure
en
spite
structure
article
determined difference poset
difference posets
1994-01
Contraexamples
1994-01-01
operation
orthoalgebraic operation
posets
example
We show that every orthoalgebra (difference orthoposet) uniquely determines a difference orthoalgebraic structure. We give examples of posets on which there exist more than one difference operation. In spite of that, every finite chain is a uniquely determined difference poset. On a difference poset there need not exist any orthoalgebraic operation, but the category of difference orthoposets is isomorphic with the category of orthoalgebras. But a difference poset which is also an orthoposet need not be a difference orthoposet. Moreover, there exist complete lattices on which there does not exist any difference operation. Finally, we show that difference operations and orthoalgebraic operations need not be extendable on a MacNeille completion of the base poset.
Contraexamples in difference posets and orthoalgebras
chain
MacNeille completion
articles
https://doi.org/10.1007/bf00671618
orthoalgebras
Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia
Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia
Applied Mathematics
Mathematical Sciences
Daniel
Bršel
International Journal of Theoretical Physics
1572-9575
0020-7748
Springer Nature
doi
10.1007/bf00671618
dimensions_id
pub.1052652300
33
1
Springer Nature - SN SciGraph project