Join-semilattices whose principal filters are pseudocomplemented
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73614847" target="_blank" >RIV/61989592:15310/22:73614847 - isvavai.cz</a>
Result on the web
<a href="http://mat76.mat.uni-miskolc.hu/mnotes/download_article/3854.pdf" target="_blank" >http://mat76.mat.uni-miskolc.hu/mnotes/download_article/3854.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.18514/MMN.2022.3854" target="_blank" >10.18514/MMN.2022.3854</a>
Alternative languages
Result language
angličtina
Original language name
Join-semilattices whose principal filters are pseudocomplemented
Original language description
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudo -complemented lattices. The pseudocomplement of a V b in the section [b, 1] is denoted by a -b and can be considered as the connective implication in a certain kind of intuitionistic logic. Contrary to the case of Brouwerian semilattices, sections need not be distributive lattices. This essentially allows possible applications in non-classical logics. We present a connection of the semilattices mentioned in the beginning with the so-called non-classical implication semilattices which can be converted into I-algebras having everywhere defined operations. Moreover, we relate our structures to sectionally and relatively residuated semilattices which means that our logical structures are closely connected with substructural logics. We show that I-algebras form a congruence distributive, 3-permutable and weakly regular variety.
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
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Miskolc Mathematical Notes
ISSN
1787-2405
e-ISSN
1787-2413
Volume of the periodical
23
Issue of the periodical within the volume
2
Country of publishing house
HU - HUNGARY
Number of pages
19
Pages from-to
"559 "- 577
UT code for WoS article
000885368300003
EID of the result in the Scopus database
2-s2.0-85143813639