Varieties whose tolerances are homomorphic images of their congruences
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arXiv
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| Format: | Preprint |
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2012
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| _version_ | 1866913568573620224 |
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| author | Czedli, Gabor Kiss, Emil W. |
| author_facet | Czedli, Gabor Kiss, Emil W. |
| contents | The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic images of their congruences (TImC). As corollaries, we prove that the variety of semilattices, all varieties of lattices, and all varieties of unary algebras have TImC. We show that a congruence n-permutable variety has TImC if and only if it is congruence permutable, and construct an idempotent variety with a majority term that fails TImC. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1204_2228 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Varieties whose tolerances are homomorphic images of their congruences Czedli, Gabor Kiss, Emil W. Rings and Algebras Primary 08A30. Secondary 08B05, 08A60, 06B10, and 20M99 The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic images of their congruences (TImC). As corollaries, we prove that the variety of semilattices, all varieties of lattices, and all varieties of unary algebras have TImC. We show that a congruence n-permutable variety has TImC if and only if it is congruence permutable, and construct an idempotent variety with a majority term that fails TImC. |
| title | Varieties whose tolerances are homomorphic images of their congruences |
| topic | Rings and Algebras Primary 08A30. Secondary 08B05, 08A60, 06B10, and 20M99 |
| url | https://arxiv.org/abs/1204.2228 |