Sectionally Pseudocomplemented Posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00118951" target="_blank" >RIV/00216224:14310/21:00118951 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989592:15310/21:73609451

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s11083-021-09555-6" target="_blank" >https://link.springer.com/article/10.1007/s11083-021-09555-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11083-021-09555-6" target="_blank" >10.1007/s11083-021-09555-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Sectionally Pseudocomplemented Posets

Popis výsledku v původním jazyce

The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension of relative pseudocomplementation for not necessarily distributive lattices. The typical example of such a lattice is the non-modular lattice N-5. The aim of this paper is to extend the concept of sectional pseudocomplementation from lattices to posets. At first we show that the class of sectionally pseudocomplemented lattices forms a variety of lattices which can be described by two simple identities. This variety has nice congruence properties. We summarize properties of sectionally pseudocomplemented posets and show differences to relative pseudocomplementation. We prove that every sectionally pseudocomplemented poset is completely L-semidistributive. We introduce the concept of congruence on these posets and show when the quotient structure becomes a poset again. Finally, we study the Dedekind-MacNeille completion of sectionally pseudocomplemented posets. We show that contrary to the case of relatively pseudocomplemented posets, this completion need not be sectionally pseudocomplemented but we present the construction of a so-called generalized ordinal sum which enables us to construct the Dedekind-MacNeille completion provided the completions of the summands are known.

Název v anglickém jazyce

Sectionally Pseudocomplemented Posets

Popis výsledku anglicky

The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension of relative pseudocomplementation for not necessarily distributive lattices. The typical example of such a lattice is the non-modular lattice N-5. The aim of this paper is to extend the concept of sectional pseudocomplementation from lattices to posets. At first we show that the class of sectionally pseudocomplemented lattices forms a variety of lattices which can be described by two simple identities. This variety has nice congruence properties. We summarize properties of sectionally pseudocomplemented posets and show differences to relative pseudocomplementation. We prove that every sectionally pseudocomplemented poset is completely L-semidistributive. We introduce the concept of congruence on these posets and show when the quotient structure becomes a poset again. Finally, we study the Dedekind-MacNeille completion of sectionally pseudocomplemented posets. We show that contrary to the case of relatively pseudocomplemented posets, this completion need not be sectionally pseudocomplemented but we present the construction of a so-called generalized ordinal sum which enables us to construct the Dedekind-MacNeille completion provided the completions of the summands are known.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Order

ISSN

0167-8094

e-ISSN

1572-9273

Svazek periodika

38

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

527-546

Kód UT WoS článku

000627203600002

EID výsledku v databázi Scopus

2-s2.0-85102456470