Residuation in lattice effect algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603174" target="_blank" >RIV/61989592:15310/20:73603174 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011419305032" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011419305032</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2019.11.008" target="_blank" >10.1016/j.fss.2019.11.008</a>
Alternative languages
Result language
angličtina
Original language name
Residuation in lattice effect algebras
Original language description
We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Also conversely, every such lattice can be converted into a lattice effect algebra and every lattice effect algebra can be reconstructed from its assigned quasiresiduated lattice. We apply this method also for lattice pseudoeffect algebras introduced by Dvureeenskij and Vetterlein. We show that every good lattice pseudoeffect algebra can be organized into a (possibly non-commutative) quasiresiduated lattice with divisibility and conversely, every such lattice can be converted into a lattice pseudoeffect algebra. Moreover, also a good lattice pseudoeffect algebra can be reconstructed from the assigned quasiresiduated lattice. (C) 2019 Elsevier B.V. All rights reserved.
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
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
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
FUZZY SETS AND SYSTEMS
ISSN
0165-0114
e-ISSN
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Volume of the periodical
397
Issue of the periodical within the volume
OCT
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
11
Pages from-to
"168 "- 178
UT code for WoS article
000562375500010
EID of the result in the Scopus database
2-s2.0-85075851904