Minimal Varieties of Representable Commutative Residuated Lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F12%3A00383374" target="_blank" >RIV/67985807:_____/12:00383374 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11225-012-9456-1" target="_blank" >http://dx.doi.org/10.1007/s11225-012-9456-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-012-9456-1" target="_blank" >10.1007/s11225-012-9456-1</a>

Result language
angličtina
Original language name
Minimal Varieties of Representable Commutative Residuated Lattices
Original language description
We solve several open problems on the cardinality of atoms in the subvariety lattice of residuated lattices and FL-algebras, we prove that the subvariety lattice of residuated lattices contains continuum many 4-potent commutative representable atoms. Analogous results apply also to atoms in the subvariety lattice of FLi-algebras and FLo-algebras. On the other hand, we show that the subvariety lattice of residuated lattices contains only five 3-potent commutative representable atoms and two integral commutative representable atoms. Inspired by the construction of atoms, we are also able to prove that the variety of integral commutative representable residuated lattices is generated by its 1-generated finite members.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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