Vol. 33, No. 2, 1970

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Projective distributive lattices

Raymond Balbes and Alfred Horn

Vol. 33 (1970), No. 2, 273–279

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
Received: 1 October 1969
Published: 1 May 1970
Raymond Balbes
Alfred Horn