Residuation in twist products and pseudo-Kleene posets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73609455" target="_blank" >RIV/61989592:15310/22:73609455 - isvavai.cz</a>
Result on the web
<a href="https://mb.math.cas.cz/full/147/3/mb147_3_7.pdf" target="_blank" >https://mb.math.cas.cz/full/147/3/mb147_3_7.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/MB.2021.0182-20" target="_blank" >10.21136/MB.2021.0182-20</a>
Alternative languages
Result language
angličtina
Original language name
Residuation in twist products and pseudo-Kleene posets
Original language description
M. Busaniche, R. Cignoli (2014), C. Tsinakis and A. M. Wille (2006) showed that every residuated lattice induces a residuation on its full twist product. For their construction they used also lattice operations. We generalize this problem to left-residuated groupoids which need not be lattice-ordered. Hence, we cannot use the same construction for the full twist product. We present another appropriate construction which, however, does not preserve commutativity and associativity of multiplication. Hence we introduce the so-called operator residuated posets to obtain another construction which preserves the mentioned properties, but the results of operators on the full twist product need not be elements, but may be subsets. We apply this construction also to restricted twist products and present necessary and sufficient conditions under which we obtain a pseudo-Kleene operator residuated poset.
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
Mathematica Bohemica
ISSN
0862-7959
e-ISSN
2464-7136
Volume of the periodical
147
Issue of the periodical within the volume
3
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
15
Pages from-to
369-383
UT code for WoS article
000712909500001
EID of the result in the Scopus database
2-s2.0-85139953921