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- Title
VARIETIES WHOSE TOLERANCES ARE HOMOMORPHIC IMAGES OF THEIR CONGRUENCES.
- Authors
CZÉDLI, GÁBOR; KISS, EMIL W.
- Abstract
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 characterise 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.
- Subjects
CONGRUENCE lattices; SEMILATTICES; UNARY algebras; SEMIGROUPS (Algebra); MODULAR lattices
- Publication
Bulletin of the Australian Mathematical Society, 2013, Vol 87, Issue 2, p326
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972712000603