Independent joins of tolerance factorable varieties

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F13%3A33146385" target="_blank" >RIV/61989592:15310/13:33146385 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00012-012-0213-0" target="_blank" >http://dx.doi.org/10.1007/s00012-012-0213-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-012-0213-0" target="_blank" >10.1007/s00012-012-0213-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Independent joins of tolerance factorable varieties

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Independent joins of tolerance factorable varieties

Popis výsledku anglicky

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.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Algebra Universalis

ISSN

0002-5240

e-ISSN

—

Svazek periodika

69

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

10

Strana od-do

83-92

Kód UT WoS článku

000318351300004

EID výsledku v databázi Scopus

—