Sectionally Pseudocomplemented Posets

J 2021

Sectionally Pseudocomplemented Posets

CHAJDA, Ivan; Helmut LÄNGER a Jan PASEKA

Základní údaje

Originální název

Sectionally Pseudocomplemented Posets

Autoři

CHAJDA, Ivan; Helmut LÄNGER a Jan PASEKA

Vydání

Order, Dordrecht, Springer, 2021, 0167-8094

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Nizozemské království

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.558

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/21:00118951

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Sectional pseudocomplementation; Poset; Congruence; Dedekind-MacNeille completion; Generalized ordinal sum

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 1. 11. 2021 09:29, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA18-06915S, projekt VaV

Název: Nové přístupy k agregačním operátorům v analýze a zpracování dat

Investor: Grantová agentura ČR, Nové přístupy k agregačním operátorům v analýze a zpracování dat

Citovat

CHAJDA, Ivan; Helmut LÄNGER a Jan PASEKA. Sectionally Pseudocomplemented Posets. Order. Dordrecht: Springer, 2021, roč. 38, č. 3, s. 527-546. ISSN 0167-8094. Dostupné z: https://doi.org/10.1007/s11083-021-09555-6.

@article{1764717,
   author = {Chajda, Ivan and Länger, Helmut and Paseka, Jan},
   article_location = {Dordrecht},
   article_number = {3},
   doi = {https://doi.org/10.1007/s11083-021-09555-6},
   keywords = {Sectional pseudocomplementation; Poset; Congruence; Dedekind-MacNeille completion; Generalized ordinal sum},
   language = {eng},
   issn = {0167-8094},
   journal = {Order},
   title = {Sectionally Pseudocomplemented Posets},
   url = {https://link.springer.com/article/10.1007/s11083-021-09555-6},
   volume = {38},
   year = {2021}
}

TY  - JOUR
ID  - 1764717
AU  - Chajda, Ivan - Länger, Helmut - Paseka, Jan
PY  - 2021
TI  - Sectionally Pseudocomplemented Posets
JF  - Order
VL  - 38
IS  - 3
SP  - 527-546
EP  - 527-546
PB  - Springer
SN  - 01678094
KW  - Sectional pseudocomplementation
KW  - Poset
KW  - Congruence
KW  - Dedekind-MacNeille completion
KW  - Generalized ordinal sum
UR  - https://link.springer.com/article/10.1007/s11083-021-09555-6
N2  - 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.
ER  -

CHAJDA, Ivan; Helmut LÄNGER a Jan PASEKA. Sectionally Pseudocomplemented Posets. \textit{Order}. Dordrecht: Springer, 2021, roč.~38, č.~3, s.~527-546. ISSN~0167-8094. Dostupné z: https://doi.org/10.1007/s11083-021-09555-6.

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