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Covering in the lattice of subuniverses of a finite distributive lattice

Part of: Lattices

Published online by Cambridge University Press:  09 April 2009

Zsolt Lengvárszky  and
George F. McNulty
Zsolt Lengvárszky
Affiliation:
Department of Computer Science, University of South Carolina, Columbia, SC 29208., USA e-mail: zlengvar@cs.sc.edu
George F. McNulty
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208.USA e-mail: mcnulty@math.sc.edu
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Abstract

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The covering relation in the lattice of subuniverses of a finite distributive lattices is characterized in terms of how new elements in a covering sublattice fit with the sublattice covered. In general, although the lattice of subuniverses of a finite distributive lattice will not be modular, nevertheless we are able to show that certain instances of Dedekind's Transposition Principle still hold. Weakly independent maps play a key role in our arguments.

Keywords

distributive latticesublatticecoveringmaximal sublattice

MSC classification

Secondary: 06B05: Structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 3 , December 1998 , pp. 333 - 353
Copyright
Copyright © Australian Mathematical Society 1998

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