Geodesic
Distributive Projective Lattices
Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 472-475

Voir la notice de l'article provenant de la source Cambridge University Press

Two basic unsolved problems of lattice theory are (1) the characterization of sublattices of free lattices and (2) the characterization of projective lattices. A solution to an important case of the first problem has been provided by Galvin and Jónsson [3], who characterize distributive sublattices of free lattices. In this paper, we solve the same case of the second problem by characterizing distributive projective lattices (Theorem 4.1). An interesting corollary is the verification for distributive lattices of the conjecture that a, finite lattice is projective if and only if it is a sublattice of a free lattice. 
Baker, Kirby A.; Hales, Alfred W. Distributive Projective Lattices. Canadian journal of mathematics, Tome 22 (1970) no. 3, pp. 472-475. doi: 10.4153/CJM-1970-054-0
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[1] 1. Balbes, R. and Horn, A., Order sums of distributive lattices, Pacific J. Math. 21 (1967), 421–435. Google Scholar

[2] 2. Dean, R., Sublattices of free lattices, Proc. Sympos. Pure Math., Vol. II, pp. 31–42 (Amer. Math. Soc, Providence, R.I., 1961). Google Scholar

[3] 3. Galvin, F. and Jonsson, B., Distributive sublattices of a free lattice, Can. J. Math. 13 (1961), 265–272. Google Scholar

[4] 4. McKenzie, R., Equational bases and non-modular lattice varieties (to appear). Google Scholar

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