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2 results

  • A Subalgebra Intersection Property for Congruence Distributive Varieties

  • Matthew A. Valeriote
  • Journal:
    Canadian Journal of Mathematics / Volume 61 / Issue 2 / 01 April 2009
    Published online by Cambridge University Press:
    20 November 2018, pp. 451-464
    Print publication:
    01 April 2009
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  • We prove that if a finite algebra $\mathbf{A}$ generates a congruence distributive variety, then the subalgebras of the powers of $\mathbf{A}$ satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem.

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

  • Part of
  • BRIAN A. DAVEY, MARCEL JACKSON, MIKLÓS MARÓTI, RALPH N. MCKENZIE
  • Journal:
    Journal of the Australian Mathematical Society / Volume 85 / Issue 1 / August 2008
    Published online by Cambridge University Press:
    01 August 2008, pp. 59-74
    Print publication:
    August 2008
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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.