Geodesic
A Finiteness Criterion for Orthomodular Lattices
Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 315-320

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

The main result of this paper is the following:THEOREM. Every finitely generated orthomodular lattice L with finitely manymaximal Boolean subalgebras (blocks) is finite.If L has one block only, our theorem reduces to the well-known fact that every finitely generated Boolean algebra is finite. On the other hand, it is known that a finitely generated orthomodular lattice without any further restrictions can be infinite. In fact, in [2] we constructed an orthomodular lattice which is generated by a three-element set with two comparable elements, has infinitely many blocks and contains an infinite chain. 
Bruns, Günter. A Finiteness Criterion for Orthomodular Lattices. Canadian journal of mathematics, Tome 30 (1978) no. 2, pp. 315-320. doi: 10.4153/CJM-1978-028-4
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[1] 1. Birkhoff, G., Lattice theory, Amer. Math. Soc. Coll. Publ. XXV (Amer. Math. Soc, Providence, 1967). Google Scholar

[2] 2. Bruns, G. and Kalmbach, G., Some remarks on free orthomodular lattices, Proc. Univ. Houston Lattice Theory Conf., Houston (1973), 397–408. Google Scholar

[3] 3. Foulis, D. J., A note on orthomodular lattices, Portugal. Math. 21 (1962), 65–72. Google Scholar

[4] 4. Holland, S. S., A Radon-Nikodym theorem for dimension lattices, Trans. Amer. Math. Soc. 108 (1963), 66–87. Google Scholar

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