About: Independent joins of tolerance factorable varieties

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	Independent joins of tolerance factorable varieties Independent joins of tolerance factorable varieties (en)
skos:prefLabel	Independent joins of tolerance factorable varieties Independent joins of tolerance factorable varieties (en)
skos:notation	RIV/61989592:15310/13:33146385!RIV14-MSM-15310___
http://linked.open...avai/riv/aktivita	O
http://linked.open...avai/riv/aktivity	O
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Halaš, Radomír Chajda, Ivan
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	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	79522
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/13:33146385
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	rectangular band; rotational lattice; product of varieties; independent join of varieties; tolerance factorable algebra; quotient algebra by a tolerance; tolerance relation (en)
http://linked.open.../riv/klicoveSlovo	independent join of varieties product of varieties quotient algebra by a tolerance rectangular band rotational lattice tolerance factorable algebra tolerance relation
http://linked.open...odStatuVydavatele	CH - Švýcarská konfederace
http://linked.open...ontrolniKodProRIV	[5D721DB1B4B4]
http://linked.open...i/riv/nazevZdroje	Algebra Universalis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	69
http://linked.open...iv/tvurceVysledku	Chajda, Ivan Halaš, Radomír Czédli, Gábor
http://linked.open...ain/vavai/riv/wos	000318351300004
issn	0002-5240
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00012-012-0213-0
http://localhost/t...ganizacniJednotka	15310

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