Weakly orthomodular and dually wekly orthomodular lattices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73590106" target="_blank" >RIV/61989592:15310/18:73590106 - 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/10.1007/s11083-017-9448-x" target="_blank" >10.1007/s11083-017-9448-x</a>
Alternative languages
Result language
angličtina
Original language name
Weakly orthomodular and dually wekly orthomodular lattices
Original language description
We introduce so-called weakly orthomodular and dually weakly orthomodular lattices which are lattices with a unary operation satisfying formally the orthomodular law or its dual although neither boundedness nor complementation is assumed. It turns out that lattices being both weakly orthomodular and dually weakly orthomodular are in fact complemented but the complementation need not be neither antitone nor an involution. Moreover, every modular lattice with complementation is both weakly orthomodular and dually weakly orthomodular. The class of weakly orthomodular lattices and the class of dually weakly orthomodular lattices form varieties which are arithmetical and congruence regular. Connections to left residuated lattices are presented and commuting elements are introduced. Using commuting elements, we define a center of such a (dually) weakly orthomodular lattice and we provide conditions under which such lattices can be represented as a non-trivial direct product.
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
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Continuities
S - Specificky vyzkum na vysokych skolach
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
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
35
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
15
Pages from-to
541-555
UT code for WoS article
000446503600010
EID of the result in the Scopus database
2-s2.0-85040639623