Varieties whose tolerances are homomorphic images of their congruences

Authors

  • Gábor Czédli Bolyai Institute of University of Szeged
  • Emil W. Kiss Loránd Eötvös University (ELTE)

Keywords:

Tolerance relation, congruence image, variety of algebras, lattices, unary algebras, semigroups, Maltsev-like condition.

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. 10.1017/S0004972712000603

Author Biographies

Gábor Czédli, Bolyai Institute of University of Szeged

Department of Algebra, Professor

Emil W. Kiss, Loránd Eötvös University (ELTE)

Department of Algebra and Number Theory, Professor

Published

2013-02-24

Issue

Vol. 87 No. 2 (2013)

Section

Articles
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