The operator of relative complementation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633267" target="_blank" >RIV/61989592:15310/25:73633267 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.worldscientific.com/doi/epdf/10.1142/S1793557125500093" target="_blank" >https://www.worldscientific.com/doi/epdf/10.1142/S1793557125500093</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S1793557125500093" target="_blank" >10.1142/S1793557125500093</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The operator of relative complementation

Popis výsledku v původním jazyce

By the operator of relative complementation is meant a mapping assigning to every element x of an interval [a, b] of a lattice L the set x(ab) of all relative complements of x in [a, b]. Of course, if L is relatively complemented then x(ab) is nonempty for each interval [a, b] and every element x belonging to it. We study the question under what condition a complement of x in L induces a relative complement of x in [a, b]. It is well-known that this is the case provided L is modular and complemented. However, we present a more general result. Further, we investigate properties of the operator of relative complementation, in particular in the case when the interval [a, b] is a modular sublattice of L or if it is finite. Moreover, we characterize when the operator (ab) of relative complementation satisfies the identity (x(ab))(ab) approximate to x provided [a, b] is complemented and we show a class of lattices where this identity holds. Finally, we establish sufficient conditions under which two different complements of a given element x of [a, b] induce the same relative complement of x in this interval.

Název v anglickém jazyce

The operator of relative complementation

Popis výsledku anglicky

By the operator of relative complementation is meant a mapping assigning to every element x of an interval [a, b] of a lattice L the set x(ab) of all relative complements of x in [a, b]. Of course, if L is relatively complemented then x(ab) is nonempty for each interval [a, b] and every element x belonging to it. We study the question under what condition a complement of x in L induces a relative complement of x in [a, b]. It is well-known that this is the case provided L is modular and complemented. However, we present a more general result. Further, we investigate properties of the operator of relative complementation, in particular in the case when the interval [a, b] is a modular sublattice of L or if it is finite. Moreover, we characterize when the operator (ab) of relative complementation satisfies the identity (x(ab))(ab) approximate to x provided [a, b] is complemented and we show a class of lattices where this identity holds. Finally, we establish sufficient conditions under which two different complements of a given element x of [a, b] induce the same relative complement of x in this interval.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF24-14386L" target="_blank" >GF24-14386L: Reprezentace algebraických sémantik pro substrukturální logiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Asian-European Journal of Mathematics

ISSN

1793-5571

e-ISSN

1793-7183

Svazek periodika

18

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

12

Strana od-do

"2550009-1"-"2550009-12"

Kód UT WoS článku

001431195700001

EID výsledku v databázi Scopus

2-s2.0-85219022462