Kleene posets and pseudo-Kleene posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612758" target="_blank" >RIV/61989592:15310/22:73612758 - isvavai.cz</a>
Result on the web
<a href="http://mat76.mat.uni-miskolc.hu/mnotes/download_article/3475.pdf" target="_blank" >http://mat76.mat.uni-miskolc.hu/mnotes/download_article/3475.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.18514/MMN.2022.3475" target="_blank" >10.18514/MMN.2022.3475</a>

Result language
angličtina
Original language name
Kleene posets and pseudo-Kleene posets
Original language description
The concept of a Kleene algebra was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebra. We extend these concepts to posets and show how (pseudo-)Kleene posets can be characterized by identities and implications of assigned commutative directoids. Moreover, we prove that the Dedekind-MacNeille completion of a finite Kleene poset is a Kleene algebra. Further, we introduce the concept of a strict (pseudo-)Kleene poset and show that under an additional assumption it can be organized into a residuated structure. Finally, we prove by using the so-called twist-product construction that every poset can be embedded into a pseudo-Kleene post in a natural way.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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