Subdirect decompositions of lattices of width two

Oscar Tivis Nelson

Vol. 24 (1968), No. 3, 519–523

DOI: 10.2140/pjm.1968.24.519

Abstract

The class of nontrivial distributive lattices is the class of subdirect products of two-element chains. Lattices of width one are distributive and hence are subdirect products of two element chains. Below it is shown that lattices of width two are subdirect products of two element chains and nonmodular lattices of order five (N₅). (width = greatest number of pairwise incomparable elements.)

Mathematical Subject Classification

Primary: 06.30

Milestones

Received: 16 January 1967

Published: 1 March 1968