| CHAJDA, Ivan, Helmut LÄNGER a Jan PASEKA. Sectionally Pseudocomplemented Posets. Online. Order. Dordrecht: Springer, 2021, roč. 38, č. 3, s. 527-546. ISSN 0167-8094. Dostupné z: https://dx.doi.org/10.1007/s11083-021-09555-6. [citováno 2024-04-23] |
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@article{1764717,
author = {Chajda, Ivan and Länger, Helmut and Paseka, Jan},
article_location = {Dordrecht},
article_number = {3},
doi = {http://dx.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. Online. \textit{Order}. Dordrecht: Springer, 2021, roč.~38, č.~3, s.~527-546. ISSN~0167-8094. Dostupné z: https://dx.doi.org/10.1007/s11083-021-09555-6. [citováno 2024-04-23]
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