Weakly orthomodular and dually wekly orthomodular lattices
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Weakly orthomodular and dually wekly orthomodular lattices
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Weakly orthomodular and dually wekly orthomodular lattices
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2018
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS
ISSN
0167-8094
e-ISSN
—
Svazek periodika
35
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
NL - Nizozemsko
Počet stran výsledku
15
Strana od-do
541-555
Kód UT WoS článku
000446503600010
EID výsledku v databázi Scopus
2-s2.0-85040639623