Varieties whose tolerances are homomorphic images of their congruences
Rings and Algebras
2024-11-01 v1
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 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.
Keywords
Cite
@article{arxiv.1204.2228,
title = {Varieties whose tolerances are homomorphic images of their congruences},
author = {Gabor Czedli and Emil W. Kiss},
journal= {arXiv preprint arXiv:1204.2228},
year = {2024}
}