Orthomodular lattices that are Z(2)-rich
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00324871" target="_blank" >RIV/68407700:21230/18:00324871 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11587-018-0378-8" target="_blank" >http://dx.doi.org/10.1007/s11587-018-0378-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11587-018-0378-8" target="_blank" >10.1007/s11587-018-0378-8</a>
Alternative languages
Result language
angličtina
Original language name
Orthomodular lattices that are Z(2)-rich
Original language description
We study the orthomodular lattices (OMLs) that have an abundance of Z(2)-valued states. We call these OMLs Z(2)-rich. Themotivation for the investigation comes from a natural algebraic curiosity that reflects the state of the (orthomodular) art, the consideration also has a certain bearing on the foundation of quantum theories (OMLs are often identified with " quantum logics") and mathematical logic (Z(2)-states are fundamental in mathematical logic). Before we launch on the subject proper, we observe, for a potential application elsewhere, that there can be a more economic introduction of Z(2)-richness - the Z(2)-richness in the orthocomplemented setup is sufficient to imply orthomodularity. In the further part we review basic examples of OMLs that are Z(2)-rich and that are not. Then we show, as a main result, that the Z(2)-rich OMLs form a large and algebraicly "friendly" class-they form a variety. In the appendix we note that the OMLs that allow for a natural introduction of a symmetric difference provide a source of another type of examples of Z(2)-rich OMLs. We also formulate open questions related to the matter studied.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS 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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Ricerche di Matematica
ISSN
0035-5038
e-ISSN
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Volume of the periodical
67
Issue of the periodical within the volume
2
Country of publishing house
IT - ITALY
Number of pages
9
Pages from-to
321-329
UT code for WoS article
000447409000002
EID of the result in the Scopus database
2-s2.0-85044459300