Orthomodular lattices that are horizontal sums of Boolean algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603117" target="_blank" >RIV/61989592:15310/20:73603117 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333183003" target="_blank" >https://obd.upol.cz/id_publ/333183003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14712/1213-7243.2020.003" target="_blank" >10.14712/1213-7243.2020.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Orthomodular lattices that are horizontal sums of Boolean algebras

Popis výsledku v původním jazyce

The paper deals with orthomodular lattices which are so-called horizontal sums of Boolean algebras. It is elementary that every such orthomodular lattice is simple and its blocks are just these Boolean algebras. Hence, the commutativity relation plays a key role and enables us to classify these orthomodular lattices. Moreover, this relation is closely related to the binary commutator which is a term function. Using the class H of horizontal sums of Boolean algebras, we establish an identity which is satisfied in the variety generated by H but not in the variety of all orthomodular lattices. The concept of ternary discriminator can be generalized for the class H in a modified version. Finally, we present several results on varieties generated by finite subsets of finite members of H.

Název v anglickém jazyce

Orthomodular lattices that are horizontal sums of Boolean algebras

Popis výsledku anglicky

The paper deals with orthomodular lattices which are so-called horizontal sums of Boolean algebras. It is elementary that every such orthomodular lattice is simple and its blocks are just these Boolean algebras. Hence, the commutativity relation plays a key role and enables us to classify these orthomodular lattices. Moreover, this relation is closely related to the binary commutator which is a term function. Using the class H of horizontal sums of Boolean algebras, we establish an identity which is satisfied in the variety generated by H but not in the variety of all orthomodular lattices. The concept of ternary discriminator can be generalized for the class H in a modified version. Finally, we present several results on varieties generated by finite subsets of finite members of H.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

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

2020

Kód důvěrnosti údajů

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

Název periodika

Commentationes Mathematicae Universitatis Carolinae

ISSN

0010-2628

e-ISSN

—

Svazek periodika

61

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

10

Strana od-do

"11 "- 20

Kód UT WoS článku

000531005700002

EID výsledku v databázi Scopus

999