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Generating sets for lattices of dimension two

✍ Scribed by Bill Sands

Publisher: Elsevier Science
Year: 1980
Tongue: English
Weight: 596 KB
Volume: 29
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90157-0

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✦ Synopsis

The dimension of a partially ordered set P is the smallest integer n (if it exists) such that the partial order on P is the intersection of n linear orders. It is shown that if L is a lattice of dimension two containing a sublattice isomorphic to the modular Iatiice Mz,+,, then every generating set of L has at least n + 2 elements. A consequence is that every finitely generated lattice of dimension two and with no infinite chains is finite.

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