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  • Mildly distributive semilattices

  • Part of
  • Robert Hickman
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 36 / Issue 3 / June 1984
    Published online by Cambridge University Press:
    09 April 2009, pp. 287-315
    Print publication:
    June 1984
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  • There is no single generalization of distributivity to semilattices. This paper investigates the class of mildly distributive semilattices, which lies between the two most commonly discussed classes in this area—weakly distributive semilattices and distributive semilattices. Particular attention is paid to describing and characterizing congruence distributive mildly distributive semilattices, in contrast to distributive semilattices, whose lattice of join partial congruences is badly behaved and which are difficult to describe.