The variety of complemented lattices where conjunction and implication form an adjoint pair
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633301" target="_blank" >RIV/61989592:15310/25:73633301 - isvavai.cz</a>
Result on the web
<a href="https://academic.oup.com/logcom/article/35/4/exaf024/8121701" target="_blank" >https://academic.oup.com/logcom/article/35/4/exaf024/8121701</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/logcom/exaf024" target="_blank" >10.1093/logcom/exaf024</a>
Alternative languages
Result language
angličtina
Original language name
The variety of complemented lattices where conjunction and implication form an adjoint pair
Original language description
The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors in [4] and [6]. In [6] there are described several classes of lattices, λ-lattices and semirings where the Sasaki operations form an adjoint pair. In the present paper we prove that the class of complemented lattices with this property forms a variety and we explicitly state its defining identities. Moreover, we prove that this variety V is congruence permutable and regular. Hence every ideal I of some member L of V is a kernel of some congruence on L. Finally, we determine a finite basis of so-called ideal terms and describe the congruence ΘI determined by the ideal I.
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>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
JOURNAL OF LOGIC AND COMPUTATION
ISSN
0955-792X
e-ISSN
1465-363X
Volume of the periodical
35
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
10
Pages from-to
"exaf024-1"-"exaf024-10"
UT code for WoS article
001477997800001
EID of the result in the Scopus database
2-s2.0-105004265877