Orthomodular and Skew Orthomodular Posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F23%3A73621161" target="_blank" >RIV/61989592:15310/23:73621161 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/15/4/810" target="_blank" >https://www.mdpi.com/2073-8994/15/4/810</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym15040810" target="_blank" >10.3390/sym15040810</a>

Result language
angličtina
Original language name
Orthomodular and Skew Orthomodular Posets
Original language description
We present the smallest non-lattice orthomodular poset and show that it is unique up to isomorphism. Since not every Boolean poset is orthomodular, we consider the class of skew orthomodular posets previously introduced by the first and third author under the name “generalized orthomodular posets”. We show that this class contains all Boolean posets and we study its subclass consisting of horizontal sums of Boolean posets. For this purpose, we introduce the concept of a compatibility relation and the so-called commutator of two elements. We show the relationship between these concepts and introduce a kind of ternary discriminator for horizontal sums of Boolean posets. Numerous examples illuminating these concepts and results are included in the paper.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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