Subalgebras of orthomodular lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00187773" target="_blank" >RIV/68407700:21230/11:00187773 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11083-010-9191-z" target="_blank" >http://dx.doi.org/10.1007/s11083-010-9191-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11083-010-9191-z" target="_blank" >10.1007/s11083-010-9191-z</a>

Result language
angličtina
Original language name
Subalgebras of orthomodular lattices
Original language description
Sachs (Can J Math 14:451-460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundations of quantum mechanics initiated by Butterfield and Isham (Int J Theor Phys 37(11): 2669-2733, 1998, Int J Theor Phys 38(3): 827-859, 1999), at least in the case where L is the orthomodular lattice of projections of a Hilbert space, or von Neumann algebra. The results here may add some additional perspective to this line of work.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
ISSN
0167-8094
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
549-563
UT code for WoS article
000300314300013
EID of the result in the Scopus database
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