Logical and algebraic properties of generalized orthomodular posets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612573" target="_blank" >RIV/61989592:15310/22:73612573 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/document/doi/10.1515/ms-2022-0018/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/ms-2022-0018/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2022-0018" target="_blank" >10.1515/ms-2022-0018</a>
Alternative languages
Result language
angličtina
Original language name
Logical and algebraic properties of generalized orthomodular posets
Original language description
Generalized orthomodular posets were introduced by D.Fazio, A.Ledda and the first author as a useful tool for studying the logic of quantum mechanics. In the present paper we study properties of these posets. In particular, we investigate conditions under which they can converted into operator residuated structures. We study their representation by means of directoidts with everywhere defined operations. We prove congruence properties for the class of algebras assigned to generalized orthomodular posets and, in particular, for a subvariety of this class determined by a simple identity. Finally, in contrast to the fact that the Dedekind-MacNeille completion of an orthomodular poset need not be an orthomodular lattice we show that the Dedekind-MacNeille completion of a strong version of a generalized orthomodular poset is nearly an orthomodular lattice.
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
—
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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematica Slovaca
ISSN
0139-9918
e-ISSN
1337-2211
Volume of the periodical
72
Issue of the periodical within the volume
2
Country of publishing house
SK - SLOVAKIA
Number of pages
12
Pages from-to
275-286
UT code for WoS article
000843844300001
EID of the result in the Scopus database
2-s2.0-85128229579