Weakly orthomodular and dually weakly orthomodular posets

Kód výsledku v 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>

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/10.1142/S1793557118500936" target="_blank" >10.1142/S1793557118500936</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Weakly orthomodular and dually weakly orthomodular posets

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Weakly orthomodular and dually weakly orthomodular posets

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Asian-European Journal of Mathematics

ISSN

1793-5571

e-ISSN

—

Svazek periodika

11

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

18

Strana od-do

"1850093-1"-"1850093-18"

Kód UT WoS článku

000427980500016

EID výsledku v databázi Scopus

2-s2.0-85044215011