Geodesic
On the Partially Ordered Set of Prime Ideals of a Distributive Lattice
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 866-874

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

For a distributive lattice L, let denote the poset of all prime ideals of L together with ∅ and L. This paper is concerned with the following type of problem. Given a class of distributive lattices, characterize all posets P for which for some . Such a poset P will be called representable over. For example, if is the class of all relatively complemented distributive lattices, then P is representable over if and only if P is a totally unordered poset with 0, 1 adjoined. One of our main results is a complete characterization of those posets P which are representable over the class of distributive lattices which are generated by their meet irreducible elements. The problem of determining which posets P are representable over the class of all distributive lattices appears to be very difficult. 
Balbes, Raymond. On the Partially Ordered Set of Prime Ideals of a Distributive Lattice. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 866-874. doi: 10.4153/CJM-1971-097-3
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