Minimal Varieties of Representable Commutative Residuated Lattices

Kód výsledku v IS VaVaI

RIV/67985807:_____/12:00383374 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1007/s11225-012-9456-1

DOI - Digital Object Identifier

10.1007/s11225-012-9456-1

Jazyk výsledku

angličtina

Název v původním jazyce

Minimal Varieties of Representable Commutative Residuated Lattices

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Minimal Varieties of Representable Commutative Residuated Lattices

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

GAP202/10/1826: Matematická fuzzy logika v informatice

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Studia Logica

ISSN

0039-3215

e-ISSN

—

Svazek periodika

100

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

1063-1078

Kód UT WoS článku

000312346600002

EID výsledku v databázi Scopus

—