Adjoint operations in twist-products of lattices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F21%3A73609271" target="_blank" >RIV/61989592:15310/21:73609271 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/13/2/253/htm" target="_blank" >https://www.mdpi.com/2073-8994/13/2/253/htm</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym13020253" target="_blank" >10.3390/sym13020253</a>
Alternative languages
Result language
angličtina
Original language name
Adjoint operations in twist-products of lattices
Original language description
Given an integral commutative residuated lattices L = (L, V, A), its full twist-product (L-2, (sic), (sic)) can be endowed with two binary operations circle dot and double right arrow introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every a is an element of L we define a certain subset P-a (L) of L-2. We characterize when Pa(L) is a sublattice of the full twist-product (L-2, (sic), (sic)). In this case P-a( L) together with some natural antitone involution ' ecomes a pseudo-Kleene lattice. If L is distributive then (P-a(L), (sic), (sic), ') becomes a Kleene lattice. We present sufficient conditions for P-a(L) being a subalgebra of (L-2,(sic), (sic), circle dot, double right arrow) and thus for and) being a pair of adjoint operations on P-a(L). Finally, we introduce another pair circle dot and double right arrow of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when P-a(L) is closed under these new operations.
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
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OECD FORD branch
10102 - Applied 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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry-Basel
ISSN
2073-8994
e-ISSN
—
Volume of the periodical
13
Issue of the periodical within the volume
2
Country of publishing house
CH - SWITZERLAND
Number of pages
13
Pages from-to
"253 "- 265
UT code for WoS article
000623197000001
EID of the result in the Scopus database
2-s2.0-85100533570