Amalgamation of Ortholattices |
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Authors: | Bruns Gunter Harding John |
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Affiliation: | (1) Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada;(2) Department of Mathematical Sciences, New Mexico State University, Las Cruses, NM, 88003, U.S.A. |
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Abstract: | We show that the variety of ortholattices has the strong amalgamation property and that the variety of orthomodular lattices has the strong Boolean amalgamation property, i.e. that two orthomodular lattices can be strongly amalgamated over a common Boolean subalgebra. We give examples to show that the variety orthomodular lattices does not have the amalgamation property and that the variety of modular ortholattices does not even have the Boolean amalgamation property. We further show that no non-Boolean variety of orthomodular lattices which is generated by orthomodular lattices of bounded height can have the Boolean amalgamation property. |
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Keywords: | ortholattice orthomodular lattice amalgamation |
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