Varieties corresponding to classes of complemented posets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609261" target="_blank" >RIV/61989592:15310/21:73609261 - isvavai.cz</a>
Result on the web
<a href="http://mat76.mat.uni-miskolc.hu/mnotes/article/3218" target="_blank" >http://mat76.mat.uni-miskolc.hu/mnotes/article/3218</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.18514/MMN.2021.3218" target="_blank" >10.18514/MMN.2021.3218</a>
Alternative languages
Result language
angličtina
Original language name
Varieties corresponding to classes of complemented posets
Original language description
As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the orthomodular law is satisfied. When we omit the condition that the complementation is an antitone involution, then we obtain skew-orthomodular posets. To each such poset we can assign a bounded λ-lattice in a non-unique way. Bounded λ-lattices are lattice-like algebras whose operations are not necessarily associative. We prove that any of the following properties for bounded posets with a unary operation can be characterized by certain identities of an arbitrary assigned λ-lattice: complementarity, orthogonality, almost skew-orthomodularity and skew-orthomodularity. Moreover, we prove corresponding independence results. Finally, we show that the variety of skew-orthomodular λ-lattices is congruence permutable as well as congruence regular.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Miskolc Mathematical Notes
ISSN
1787-2405
e-ISSN
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Volume of the periodical
22
Issue of the periodical within the volume
2
Country of publishing house
HU - HUNGARY
Number of pages
13
Pages from-to
611-623
UT code for WoS article
000741090800009
EID of the result in the Scopus database
2-s2.0-85108008019