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VARIETIES WHOSE TOLERANCES ARE HOMOMORPHIC IMAGES OF THEIR CONGRUENCES

Part of: Lattices Semigroups Algebraic structures

Published online by Cambridge University Press:  08 August 2012

GÁBOR CZÉDLI  and
EMIL W. KISS
GÁBOR CZÉDLI*
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary (email: czedli@math.u-szeged.hu)
EMIL W. KISS
Affiliation:
Department of Algebra and Number Theory, Eötvös University, Pázmány Péter sétány 1/c, 1117 Budapest, Hungary (email: ewkiss@cs.elte.hu)
*
✉For correspondence; e-mail: czedli@math.u-szeged.hu
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Abstract

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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.

Keywords

tolerance relationcongruence imagevariety of algebraslatticesunary algebrassemigroupsMalcev-like condition

MSC classification

Secondary: 08A30: Subalgebras, congruence relations 08A60: Unary algebras 06B10: Ideals, congruence relations 20M99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 326 - 338
Copyright
©2012 Australian Mathematical Publishing Association Inc.

Footnotes

Dedicated to Béla Csákány on his eightieth birthday

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