Sectionally Pseudocomplemented Posets
The result's identifiers
Result code in 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>
Alternative codes found
RIV/61989592:15310/21:73609451
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Sectionally Pseudocomplemented Posets
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Order
ISSN
0167-8094
e-ISSN
1572-9273
Volume of the periodical
38
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
20
Pages from-to
527-546
UT code for WoS article
000627203600002
EID of the result in the Scopus database
2-s2.0-85102456470