Geodesic
On the Structure of Finitely Presented Lattices
Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 404-411

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

A lattice L is finitely presented (or presentable) if and only if it can be described with finitely many generators and finitely many relations. Equivalently, L is the lattice freely generated by a finite partial lattice A, in notation, L = F(A). (For more detail, see Section 1.5 of [6].)It is an old “conjecture” of lattice theory that in a finitely presented (or presentable) lattice the elements behave “freely” once we get far enough from the generators.In this paper we prove a structure theorem that could be said to verify this conjecture.THEOREM 1. Let L be a finitely presentable lattice. Then there exists a congruence relation θ such that L/θ is finite and each congruence class is embeddable in a free lattice. 
Gratzer, G.; Huhn, A. P.; Lakser, H. On the Structure of Finitely Presented Lattices. Canadian journal of mathematics, Tome 33 (1981) no. 2, pp. 404-411. doi: 10.4153/CJM-1981-035-5
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