Left residuated lattices induced by lattices with a unary oparation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603114" target="_blank" >RIV/61989592:15310/20:73603114 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00500-019-04461-x" target="_blank" >https://link.springer.com/article/10.1007/s00500-019-04461-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-019-04461-x" target="_blank" >10.1007/s00500-019-04461-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Left residuated lattices induced by lattices with a unary oparation

Popis výsledku v původním jazyce

In a previous paper, the authors defined two binary term operations in orthomodular lattices such that an orthomodular lattice can be organized by means of them into a left residuated lattice. It is a natural question if these operations serve in this way also for more general lattices than the orthomodular ones. In our present paper, we involve two conditions formulated as simple identities in two variables under which this is really the case. Hence, we obtain a variety of lattices with a unary operation which contains exactly those lattices with a unary operation which can be converted into a left residuated lattice by use of the above mentioned operations. It turns out that every lattice in this variety is in fact a bounded one and the unary operation is a complementation. Finally, we use a similar technique by using simpler terms and identities motivated by Boolean algebras.

Název v anglickém jazyce

Left residuated lattices induced by lattices with a unary oparation

Popis výsledku anglicky

In a previous paper, the authors defined two binary term operations in orthomodular lattices such that an orthomodular lattice can be organized by means of them into a left residuated lattice. It is a natural question if these operations serve in this way also for more general lattices than the orthomodular ones. In our present paper, we involve two conditions formulated as simple identities in two variables under which this is really the case. Hence, we obtain a variety of lattices with a unary operation which contains exactly those lattices with a unary operation which can be converted into a left residuated lattice by use of the above mentioned operations. It turns out that every lattice in this variety is in fact a bounded one and the unary operation is a complementation. Finally, we use a similar technique by using simpler terms and identities motivated by Boolean algebras.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

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

SOFT COMPUTING

ISSN

1432-7643

e-ISSN

—

Svazek periodika

24

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

7

Strana od-do

"723 "- 729

Kód UT WoS článku

000493720400003

EID výsledku v databázi Scopus

2-s2.0-85097024235