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PATH-CONNECTED AND NON PATH-CONNECTED ORTHOMODULAR LATTICES
- Authors
- Park, Eunsoon; Song, Wonhee
- Issue Date
- Sep-2009
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- orthomodular lattice; with finite sites; path-connected; non path-connected; Boolean algebra
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.46, no.5, pp.845 - 856
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 46
- Number
- 5
- Start Page
- 845
- End Page
- 856
- ISSN
- 1015-8634
- Abstract
- A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A boolean AND B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if vertical bar A boolean AND B vertical bar < infinity for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [Com L]v generated by the commutators of L is finite, then L is pathconnected.
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