Geodesic
Some Finiteness Conditions for Orthomodular Lattices
Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 535-549

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Throughout this paper L will be an orthomodular lattice and the set of all maximal Boolean subalgebras, also called blocks [4], of L. For every x ∈ L, C(x) will be the set of all elements of L which commute with x. Let n ≧ 1 be a natural number. In this paper we consider the following conditions for L: A n : L has at most n blocks, B n : there exists a covering of L by at most n blocks, C n: the set {C(x)| x ∈ L} has at most n elements, D n : out of any n + 1 elements of L at least two commute.We also consider quantified versions of these statements, namely the statements A, B, C, D defined by: A ⇔ ∃ n An , B ⇔ ∃ n Bn , C ⇔ ∃ n Cn and D ⇔ ∃ n Dn . 
Bruns, Günter; Greechie, Richard. Some Finiteness Conditions for Orthomodular Lattices. Canadian journal of mathematics, Tome 34 (1982) no. 3, pp. 535-549. doi: 10.4153/CJM-1982-038-2
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