Geodesic
On Finitely Generated Lattices of Finite Width
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 28-48

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

The width of a lattice L is the maximum number of pairwise noncomparable elements in L.It has been known for some time ([5] ; see also [4]) that there is just one subdirectly irreducible lattice of width twro, namely the five-element nonmodular lattice N 5. It follows that every lattice of width two is in the variety of N 5, and that every finitely generated lattice of width two is finite.Beginning a study of lattices of width three, W. Poguntke [6] showed that there are infinitely many finite simple lattices of width three. Further studies on width three lattices were made in [3], where it was asked whether every finitely generated simple lattice of width three is finite. In this paper we will show that, in fact, more is true:THEOREM 1.1. Every finitely generated subdirectly irreducible lattice of width three is finite. 
Poguntke, W.; Sands, B. On Finitely Generated Lattices of Finite Width. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 28-48. doi: 10.4153/CJM-1981-004-5
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