About: Minimal Varieties of Representable Commutative Residuated Lattices

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. 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. (en)
Title	Minimal Varieties of Representable Commutative Residuated Lattices Minimal Varieties of Representable Commutative Residuated Lattices (en)
skos:prefLabel	Minimal Varieties of Representable Commutative Residuated Lattices Minimal Varieties of Representable Commutative Residuated Lattices (en)
skos:notation	RIV/67985807:_____/12:00383374!RIV13-GA0-67985807
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP202/10/1826), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Horčík, Rostislav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	150646
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/12:00383374
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	commutative residuated lattice; subvariety lattice; minimal variety; substructural logic; maximally consistent logic (en)
http://linked.open.../riv/klicoveSlovo	commutative residuated lattice maximally consistent logic minimal variety subvariety lattice substructural logic
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[EABA891789F6]
http://linked.open...i/riv/nazevZdroje	Studia Logica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Matematická fuzzy logika v informatice
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	100
http://linked.open...iv/tvurceVysledku	Horčík, Rostislav
http://linked.open...ain/vavai/riv/wos	000312346600002
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	0039-3215
number of pages	16 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s11225-012-9456-1

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