Geodesic
A remark on $\lambda$-regular orthomodular lattices
Applications of Mathematics, Tome 34 (1989) no. 6, pp. 449-452
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A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality $k$ is called $\lambda$-regular, if each atom is a member of just $\lambda$ blocks. We estimate the minimal number of blocks of $\lambda$-regular orthomodular lattices to be lower than of equal to $\lambda^2$ regardless of $k$.
A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality $k$ is called $\lambda$-regular, if each atom is a member of just $\lambda$ blocks. We estimate the minimal number of blocks of $\lambda$-regular orthomodular lattices to be lower than of equal to $\lambda^2$ regardless of $k$.
DOI : 10.21136/AM.1989.104375
Classification : 03G12, 05C65, 06C15
Keywords: Greechie diagram; finite orthomodular lattice; maximal Boolean subalgebra 
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Rogalewicz, Vladimír. A remark on $\lambda$-regular orthomodular lattices. Applications of Mathematics, Tome 34 (1989) no. 6, pp. 449-452. doi: 10.21136/AM.1989.104375

[1] M. Dichtl: Astroids and pastings. Algebra Universalis 18 (1984), 380-385. | DOI | MR | Zbl

[2] R. J. Greechie: Orthomodular lattices admitting no states. J. Combinatorial Theory 10 (1971), 119-132. | DOI | MR | Zbl

[3] G. Kalmbach: Orthomodular Lattices. Academic Press, London, 1984. | MR | Zbl

[4] E. Köhler: Orthomodulare Verbände rnit Regularitätsbedingungen. J. of Geometry 119 (1982), 130-145. | DOI | MR

[5] M. Navara V. Rogalewicz: The pasting constructions for Orthomodular posets. Submitted for publication.

[6] V. Rogalewicz: Any orthomodular poset is a pasting of Boolean algebras. Comment. Math. Univ. Carol. 29 (1988), 557-558. | MR | Zbl

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