Varieties corresponding to classes of complemented posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609261" target="_blank" >RIV/61989592:15310/21:73609261 - isvavai.cz</a>

Výsledek na webu

<a href="http://mat76.mat.uni-miskolc.hu/mnotes/article/3218" target="_blank" >http://mat76.mat.uni-miskolc.hu/mnotes/article/3218</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.18514/MMN.2021.3218" target="_blank" >10.18514/MMN.2021.3218</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Varieties corresponding to classes of complemented posets

Popis výsledku v původním jazyce

As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the orthomodular law is satisfied. When we omit the condition that the complementation is an antitone involution, then we obtain skew-orthomodular posets. To each such poset we can assign a bounded λ-lattice in a non-unique way. Bounded λ-lattices are lattice-like algebras whose operations are not necessarily associative. We prove that any of the following properties for bounded posets with a unary operation can be characterized by certain identities of an arbitrary assigned λ-lattice: complementarity, orthogonality, almost skew-orthomodularity and skew-orthomodularity. Moreover, we prove corresponding independence results. Finally, we show that the variety of skew-orthomodular λ-lattices is congruence permutable as well as congruence regular.

Název v anglickém jazyce

Varieties corresponding to classes of complemented posets

Popis výsledku anglicky

As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the orthomodular law is satisfied. When we omit the condition that the complementation is an antitone involution, then we obtain skew-orthomodular posets. To each such poset we can assign a bounded λ-lattice in a non-unique way. Bounded λ-lattices are lattice-like algebras whose operations are not necessarily associative. We prove that any of the following properties for bounded posets with a unary operation can be characterized by certain identities of an arbitrary assigned λ-lattice: complementarity, orthogonality, almost skew-orthomodularity and skew-orthomodularity. Moreover, we prove corresponding independence results. Finally, we show that the variety of skew-orthomodular λ-lattices is congruence permutable as well as congruence regular.

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

2021

Kód důvěrnosti údajů

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

Název periodika

Miskolc Mathematical Notes

ISSN

1787-2405

e-ISSN

—

Svazek periodika

22

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

13

Strana od-do

611-623

Kód UT WoS článku

000741090800009

EID výsledku v databázi Scopus

2-s2.0-85108008019