Journal of the Australian Mathematical Society

Research Article

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

BRIAN A. DAVEYa1, MARCEL JACKSONa2 c1, MIKLÓS MARÓTIa3 and RALPH N. MCKENZIEa4

a1 Department of Mathematics, La Trobe University, Victoria, Australia (email: b.davey@latrobe.edu.au)

a2 Department of Mathematics, La Trobe University, Victoria, Australia (email: m.g.jackson@latrobe.edu.au)

a3 János Bolyai Mathematical Institute, University of Szeged, Szeged, Hungary (email: mmaroti@math.u-szeged.hu)

a4 Department of Mathematics, Vanderbilt University, Nashville, TN, USA (email: mckenzie@math.vanderbilt.edu)

Abstract

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 under the additional assumption that the variety is residually very finite.

(Received August 30 2006)

(Accepted February 23 2007)

2000 Mathematics subject classification

  • 08B10

Keywords and phrases

  • finitely determined syntactic congruences;
  • term finite principal congruences;
  • finite principal length;
  • congruence distributive;
  • congruence modular;
  • congruence permutable

Correspondence:

c1 For correspondence; e-mail: m.g.jackson@latrobe.edu.au

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.