On locally finite orthomodular lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00367663" target="_blank" >RIV/68407700:21230/23:00367663 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/ms-2023-0040" target="_blank" >https://doi.org/10.1515/ms-2023-0040</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2023-0040" target="_blank" >10.1515/ms-2023-0040</a>

Result language
angličtina
Original language name
On locally finite orthomodular lattices
Original language description
Let us denote by LF the class of all orthomodular lattices (OMLs) that are locally finite (i.e., L element LF provided each finite subset of L generates in L a finite subOML). In this note, we first show how one can obtain new locally finite OMLs from the initial ones and enlarge thus the class LF. We find LF considerably large though, obviously, not all OMLs belong to LF. Then we study states on the OMLs of LF. We show that local finiteness may to a certain extent make up for distributivity. For instance, we show that if L element LF and if for any finite subOML K there is a state s: K -> [0,1] on K, then there is a state on the entire L. We also consider further algebraic and state properties of LF relevant to the quantum logic theory.
Czech name
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Czech description
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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

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)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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