Properties and Special Filters of Pseudocomplemented Posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633209" target="_blank" >RIV/61989592:15310/25:73633209 - isvavai.cz</a>

Výsledek na webu

<a href="https://arxiv.org/pdf/2312.04685v1" target="_blank" >https://arxiv.org/pdf/2312.04685v1</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Properties and Special Filters of Pseudocomplemented Posets

Popis výsledku v původním jazyce

Investigating the structure of pseudocomplemented lattices started and this structure was essentially developed by G. Gratzer. In recent years, some special filters in pseudocomplemented and Stone lattices have been studied by M. Sambasiva Rao. However, in some applications, in particular in non-classical logics with unsharp logical connectives, pseudocomplemented posets instead of lattices are used. This motivated us to develop an algebraic theory of pseudocomplemented posets, i.e. we derive identities and inequalities holding in such posets and we use them in order to characterize the so-called Stone posets. Then we adopt several concepts of special filters and we investigate their properties in pseudocomplemented posets. Moreover, we show how properties of these filters influence algebraic properties of the underlying pseudocomplemented posets.

Název v anglickém jazyce

Properties and Special Filters of Pseudocomplemented Posets

Popis výsledku anglicky

Investigating the structure of pseudocomplemented lattices started and this structure was essentially developed by G. Gratzer. In recent years, some special filters in pseudocomplemented and Stone lattices have been studied by M. Sambasiva Rao. However, in some applications, in particular in non-classical logics with unsharp logical connectives, pseudocomplemented posets instead of lattices are used. This motivated us to develop an algebraic theory of pseudocomplemented posets, i.e. we derive identities and inequalities holding in such posets and we use them in order to characterize the so-called Stone posets. Then we adopt several concepts of special filters and we investigate their properties in pseudocomplemented posets. Moreover, we show how properties of these filters influence algebraic properties of the underlying pseudocomplemented posets.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

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

JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING

ISSN

1542-3980

e-ISSN

1542-3999

Svazek periodika

44

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

"269 "- 289

Kód UT WoS článku

001415618800004

EID výsledku v databázi Scopus

2-s2.0-85215541888