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Mildly distributive semilattices

Part of: Ordered sets Distributive lattices Boolean algebras (Boolean rings)

Published online by Cambridge University Press:  09 April 2009

Robert Hickman
Robert Hickman
Affiliation:
Department of Pure Mathematics, University of SydneyN.S.W. 2006, Australia
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Abstract

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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.

Keywords

mildly distributiveweakly distributivestrong idealfilterjoin partial congruenceconnected semilattice.

MSC classification

Secondary: 06A12: Semilattices 06D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 3 , June 1984 , pp. 287 - 315
Copyright
Copyright © Australian Mathematical Society 1984

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