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PRINCIPAL AND SYNTACTIC CONGRUENCES IN CONGRUENCE-DISTRIBUTIVE AND CONGRUENCE-PERMUTABLE VARIETIES

Part of: Varieties

Published online by Cambridge University Press:  01 August 2008

BRIAN A. DAVEY ,
MARCEL JACKSON ,
MIKLÓS MARÓTI  and
RALPH N. MCKENZIE
BRIAN A. DAVEY
Affiliation:
Department of Mathematics, La Trobe University, Victoria, Australia (email: b.davey@latrobe.edu.au)
MARCEL JACKSON*
Affiliation:
Department of Mathematics, La Trobe University, Victoria, Australia (email: m.g.jackson@latrobe.edu.au)
MIKLÓS MARÓTI
Affiliation:
János Bolyai Mathematical Institute, University of Szeged, Szeged, Hungary (email: mmaroti@math.u-szeged.hu)
RALPH N. MCKENZIE
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN, USA (email: mckenzie@math.vanderbilt.edu)
*
✉For correspondence; e-mail: m.g.jackson@latrobe.edu.au
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Abstract

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We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even underthe additional assumption that the variety is residually very finite.

Keywords

finitely determined syntactic congruencesterm finite principal congruencesfinite principal lengthcongruence distributivecongruence modularcongruence permutable

MSC classification

Secondary: 08B10: Congruence modularity, congruence distributivity
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 1 , August 2008 , pp. 59 - 74
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The second author was supported by ARC Discovery Project Grant DP0342459. The third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 37877 and T 48809.

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