Projective distributive lattices

Raymond Balbes and Alfred Horn

Vol. 33 (1970), No. 2, 273–279

DOI: 10.2140/pjm.1970.33.273

Abstract

It will be shown that a countable distributive lattice is projective if and only if the product of any two join irreducible elements is join irreducible, and every element of the lattice is both a finite sum of join irreducible elements and a finite product of meet irreducible elements. For an arbitrary distributive lattice, necessary and sufficient conditions for projectivity are obtained by adding to these conditions a further condition on the set of join irreducible elements.

Mathematical Subject Classification

Primary: 06.50

Milestones

Received: 1 October 1969

Published: 1 May 1970