Independent joins of tolerance factorable varieties
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2012
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| _version_ | 1866914999635542016 |
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| author | Chajda, Ivan Czédli, Gábor Halas, Radomir |
| author_facet | Chajda, Ivan Czédli, Gábor Halas, Radomir |
| contents | Let L denote the variety of lattices. In 1982, the second author proved that L is strongly tolerance factorable, that is, the members of L have quotients in L modulo tolerances, although L 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.\ Czédli and G.\ Grätzer, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1207_1732 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Independent joins of tolerance factorable varieties Chajda, Ivan Czédli, Gábor Halas, Radomir Rings and Algebras Primary: 08A30. Secondary: 08B99, 06B10, 20M07 Let L denote the variety of lattices. In 1982, the second author proved that L is strongly tolerance factorable, that is, the members of L have quotients in L modulo tolerances, although L 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.\ Czédli and G.\ Grätzer, 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. |
| title | Independent joins of tolerance factorable varieties |
| topic | Rings and Algebras Primary: 08A30. Secondary: 08B99, 06B10, 20M07 |
| url | https://arxiv.org/abs/1207.1732 |