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Statements

Subject Item
n2:RIV%2F61989592%3A15310%2F13%3A33146385%21RIV14-MSM-15310___
rdf:type
n7:Vysledek skos:Concept
dcterms:description
Let Lat denote the variety of lattices. In 1982, the second author proved that Lat is strongly tolerance factorable, that is, the members of Lat have quotients in Lat modulo tolerances, although Lat has proper tolerances. We did not know any other nontrivial example of a strongly tolerance factorable variety. Now we prove that this property is preserved by forming independent joins (also called products) of varieties. This enables us to present infinitely many strongly tolerance factorable varieties with proper tolerances. Extending a recent result of G. Czedli and G. Gratzer, we show that if V is a strongly tolerance factorable variety, then the tolerances of V are exactly the homomorphic images of congruences of algebras in V. Our observation that (strong) tolerance factorability is not necessarily preserved when passing from a variety to an equivalent one leads to an open problem. Let Lat denote the variety of lattices. In 1982, the second author proved that Lat is strongly tolerance factorable, that is, the members of Lat have quotients in Lat modulo tolerances, although Lat has proper tolerances. We did not know any other nontrivial example of a strongly tolerance factorable variety. Now we prove that this property is preserved by forming independent joins (also called products) of varieties. This enables us to present infinitely many strongly tolerance factorable varieties with proper tolerances. Extending a recent result of G. Czedli and G. Gratzer, we show that if V is a strongly tolerance factorable variety, then the tolerances of V are exactly the homomorphic images of congruences of algebras in V. Our observation that (strong) tolerance factorability is not necessarily preserved when passing from a variety to an equivalent one leads to an open problem.
dcterms:title
Independent joins of tolerance factorable varieties Independent joins of tolerance factorable varieties
skos:prefLabel
Independent joins of tolerance factorable varieties Independent joins of tolerance factorable varieties
skos:notation
RIV/61989592:15310/13:33146385!RIV14-MSM-15310___
n7:predkladatel
n10:orjk%3A15310
n3:aktivita
n16:O
n3:aktivity
O
n3:cisloPeriodika
1
n3:dodaniDat
n5:2014
n3:domaciTvurceVysledku
n19:9055819 n19:3213145
n3:druhVysledku
n14:J
n3:duvernostUdaju
n9:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
79522
n3:idVysledku
RIV/61989592:15310/13:33146385
n3:jazykVysledku
n18:eng
n3:klicovaSlova
rectangular band; rotational lattice; product of varieties; independent join of varieties; tolerance factorable algebra; quotient algebra by a tolerance; tolerance relation
n3:klicoveSlovo
n4:quotient%20algebra%20by%20a%20tolerance n4:rotational%20lattice n4:product%20of%20varieties n4:tolerance%20factorable%20algebra n4:rectangular%20band n4:tolerance%20relation n4:independent%20join%20of%20varieties
n3:kodStatuVydavatele
CH - Švýcarská konfederace
n3:kontrolniKodProRIV
[5D721DB1B4B4]
n3:nazevZdroje
Algebra Universalis
n3:obor
n12:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n5:2013
n3:svazekPeriodika
69
n3:tvurceVysledku
Czédli, Gábor Halaš, Radomír Chajda, Ivan
n3:wos
000318351300004
s:issn
0002-5240
s:numberOfPages
10
n11:doi
10.1007/s00012-012-0213-0
n13:organizacniJednotka
15310