Weakly orthomodular and dually weakly orthomodular posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73590048" target="_blank" >RIV/61989592:15310/18:73590048 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs11083-017-9448-x.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs11083-017-9448-x.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1793557118500936" target="_blank" >10.1142/S1793557118500936</a>

Result language
angličtina
Original language name
Weakly orthomodular and dually weakly orthomodular posets
Original language description
Orthomodular posets form an algebraic semantic for the logic of quantum mechanics. We show several methods how to construct orthomodular posets via a representation within the powerset of a given set. Further, we generalize this concept to the concept of weakly orthomodular and dually weakly orthomodular posets where the complementation need not be antitone or an involution. We show several interesting examples of such posets and prove which intervals of these posets are weakly orthomodular or dually weakly orthomodular again. To every (dually) weakly orthomodular poset can be assigned an algebra with total operations, a so-called (dually) weakly orthomodular lambda-lattice. We study properties of these lambda-lattices and show that the variety of these.-lattices has nice congruence properties.
Czech name
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Czech description
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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

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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