Geodesic
Orthomodular Lattices Which can be Covered by Finitely Many Blocks
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 696-699

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

In our paper [3] we considered four nniteness conditions for an orthomodular lattice (abbreviated: OML) L and conjectured their equivalence. The only question left open in that paper was whether an OML L which can be covered by finitely many blocks (maximal Boolean subalgebras) has only finitely many blocks. In this paper we give an affirmative answer to this question, in fact, we prove the slightly stronger result: 
Bruns, Günter; Greechie, Richard. Orthomodular Lattices Which can be Covered by Finitely Many Blocks. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 696-699. doi: 10.4153/CJM-1982-047-1
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[1] 1. Brouwer, A. E., An inequality for binary vector spaces (manuscript). Google Scholar

[2] 2. Bruns, G., Covering a Boolean algebra by subalgebras, Mathematisches Forschungsinstitut Oberwolfach, Tagungsbericht 23 (1980). Google Scholar

[3] 3. Bruns, G. and Greechie, R., Some finiteness conditions for orthomodular lattices, Can. J. Math. 34 (1982), 535–549. Google Scholar

[4] 4. Greechie, R., On generating distributive sublattices of orthomodular lattices, Proc. AMS 67 (1977), 17–22. Google Scholar

5. An addendum to On generating distributive sublattices of orthomodular lattices, Proc. AMS 76 (1979), 216–218. Google Scholar

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