C-ideals in complemented posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73621057" target="_blank" >RIV/61989592:15310/24:73621057 - isvavai.cz</a>

Výsledek na webu

<a href="https://mbpapers.math.cas.cz/full/149/3/mb149_3_3.pdf" target="_blank" >https://mbpapers.math.cas.cz/full/149/3/mb149_3_3.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/MB.2023.0108-22" target="_blank" >10.21136/MB.2023.0108-22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

C-ideals in complemented posets

Popis výsledku v původním jazyce

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.

Název v anglickém jazyce

C-ideals in complemented posets

Popis výsledku anglicky

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive pseudocomplemented lattices and semilattices by several authors, see References. Now we apply this concept of a c-ideal (dually, c-filter) to complemented posets where the complementation need neither be antitone nor an involution, but still satisfies some weak conditions. We show when an ideal or filter in such a poset is a c-ideal or c-filter, and we prove basic properties of them. Finally, we prove the so-called separation theorems for c-ideals. The text is illustrated by several examples.

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

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematica Bohemica

ISSN

0862-7959

e-ISSN

2464-7136

Svazek periodika

149

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

12

Strana od-do

305-316

Kód UT WoS článku

001023524300001

EID výsledku v databázi Scopus

2-s2.0-85205872224