Logical and algebraic properties of generalized orthomodular posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73612573" target="_blank" >RIV/61989592:15310/22:73612573 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.degruyter.com/document/doi/10.1515/ms-2022-0018/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/ms-2022-0018/html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2022-0018" target="_blank" >10.1515/ms-2022-0018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Logical and algebraic properties of generalized orthomodular posets

Popis výsledku v původním jazyce

Generalized orthomodular posets were introduced by D.Fazio, A.Ledda and the first author as a useful tool for studying the logic of quantum mechanics. In the present paper we study properties of these posets. In particular, we investigate conditions under which they can converted into operator residuated structures. We study their representation by means of directoidts with everywhere defined operations. We prove congruence properties for the class of algebras assigned to generalized orthomodular posets and, in particular, for a subvariety of this class determined by a simple identity. Finally, in contrast to the fact that the Dedekind-MacNeille completion of an orthomodular poset need not be an orthomodular lattice we show that the Dedekind-MacNeille completion of a strong version of a generalized orthomodular poset is nearly an orthomodular lattice.

Název v anglickém jazyce

Logical and algebraic properties of generalized orthomodular posets

Popis výsledku anglicky

Generalized orthomodular posets were introduced by D.Fazio, A.Ledda and the first author as a useful tool for studying the logic of quantum mechanics. In the present paper we study properties of these posets. In particular, we investigate conditions under which they can converted into operator residuated structures. We study their representation by means of directoidts with everywhere defined operations. We prove congruence properties for the class of algebras assigned to generalized orthomodular posets and, in particular, for a subvariety of this class determined by a simple identity. Finally, in contrast to the fact that the Dedekind-MacNeille completion of an orthomodular poset need not be an orthomodular lattice we show that the Dedekind-MacNeille completion of a strong version of a generalized orthomodular poset is nearly an orthomodular lattice.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

1337-2211

Svazek periodika

72

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

12

Strana od-do

275-286

Kód UT WoS článku

000843844300001

EID výsledku v databázi Scopus

2-s2.0-85128229579