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2 results

  • VARIETIES WHOSE TOLERANCES ARE HOMOMORPHIC IMAGES OF THEIR CONGRUENCES

  • Part of
  • GÁBOR CZÉDLI, EMIL W. KISS
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 87 / Issue 2 / April 2013
    Published online by Cambridge University Press:
    08 August 2012, pp. 326-338
    Print publication:
    April 2013
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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.

  • Strong and full dualisability: three-element unary algebras

  • Part of
  • J. G. Pitkethly
  • Journal:
    Journal of the Australian Mathematical Society / Volume 73 / Issue 2 / October 2002
    Published online by Cambridge University Press:
    09 April 2009, pp. 187-220
    Print publication:
    October 2002
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  • We characterise the strongly dualisable three-element unary algebras and show that every fully dualisable three-element unary algebra is strongly dualisable. It follows from the characterisation that, for dualisable three-element unary algebras, strong dualisability is equivalent to a weak form of injectivity.