States On Orthocomplemented Difference Posets (Extensions)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00300847" target="_blank" >RIV/68407700:21230/16:00300847 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11005-016-0862-6" target="_blank" >http://dx.doi.org/10.1007/s11005-016-0862-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11005-016-0862-6" target="_blank" >10.1007/s11005-016-0862-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

States On Orthocomplemented Difference Posets (Extensions)

Popis výsledku v původním jazyce

We continue the investigation of orthocomplemented posets that are endowed with a symmetric difference (ODPs). The ODPs are orthomodular and, therefore, can be viewed as "enriched" quantum logics. In this note, we introduced states on ODPs. We derive their basic properties and study the possibility of extending them over larger ODPs. We show that there are extensions of states from Boolean algebras over unital ODPs. Since unital ODPs do not, in general, have to be set-representable, this result can be applied to a rather large class of ODPs. We then ask the same question after replacing Boolean algebras with "nearly Boolean" ODPs (the pseudocomplemented ODPs). Making use of a few results on ODPs, some known and some new, we construct a pseudocomplemented ODP, P, and a state on P that does not allow for extensions over larger ODPs.

Název v anglickém jazyce

States On Orthocomplemented Difference Posets (Extensions)

Popis výsledku anglicky

We continue the investigation of orthocomplemented posets that are endowed with a symmetric difference (ODPs). The ODPs are orthomodular and, therefore, can be viewed as "enriched" quantum logics. In this note, we introduced states on ODPs. We derive their basic properties and study the possibility of extending them over larger ODPs. We show that there are extensions of states from Boolean algebras over unital ODPs. Since unital ODPs do not, in general, have to be set-representable, this result can be applied to a rather large class of ODPs. We then ask the same question after replacing Boolean algebras with "nearly Boolean" ODPs (the pseudocomplemented ODPs). Making use of a few results on ODPs, some known and some new, we construct a pseudocomplemented ODP, P, and a state on P that does not allow for extensions over larger ODPs.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Letters in Mathematical Physics

ISSN

0377-9017

e-ISSN

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Svazek periodika

106

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

7

Strana od-do

1131-1137

Kód UT WoS článku

000379609000006

EID výsledku v databázi Scopus

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