Boolean subalgebras of orthoalgebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F19%3A00335506" target="_blank" >RIV/68407700:21230/19:00335506 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11083-019-09483-6" target="_blank" >https://doi.org/10.1007/s11083-019-09483-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11083-019-09483-6" target="_blank" >10.1007/s11083-019-09483-6</a>
Alternative languages
Result language
angličtina
Original language name
Boolean subalgebras of orthoalgebras
Original language description
We develop a direct method to recover an orthoalgebra from its poset of Boolean subalgebras. For this a new notion of direction is introduced. Directions are also used to characterize in purely order-theoretic terms those posets that are isomorphic to the poset of Boolean subalgebras of an orthoalgebra. These posets are characterized by simple conditions defining orthodomains and the additional requirement of having enough directions. Excepting pathologies involving maximal Boolean subalgebras of four elements, it is shown that there is an equivalence between the category of orthoalgebras and the category of orthodomains with enough directions with morphisms suitably defined. Furthermore, we develop a representation of orthodomains with enough directions, and hence of orthoalgebras, as certain hypergraphs. This hypergraph approach extends the technique of Greechie diagrams and resembles projective geometry. Using such hypergraphs, every orthomodular poset can be represented by a set of points and lines where each line contains exactly three points.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
ISSN
0167-8094
e-ISSN
1572-9273
Volume of the periodical
36
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
47
Pages from-to
563-609
UT code for WoS article
000509936700010
EID of the result in the Scopus database
2-s2.0-85062777699