Independent joins of tolerance factorable varieties

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Independent joins of tolerance factorable varieties
Original language 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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