AustMS

Journals

JAMS-A

JAMS-B

JAMS-E

Bulletin

Gazette

Journal of the Australian Mathematical Society - Series A
Vol. 65 Part 3 (1998)

Covering in the lattice of subuniverses of a finite distributive lattice

Zsolt Lengvárszky
Department of Computer Science
University of South Carolina
Columbia, SC 29208. USA
and
George F. McNulty
Department of Mathematics
University of South Carolina
Columbia, SC 29208. USA

Abstract:

The covering relation in the lattice of subuniverses of a finite distributive lattice 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.

View Paper in
PDF Format

PDF file size: 145K


© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
1998-09-18