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A note on constructible lattices

Published online by Cambridge University Press:  09 April 2009

D. H. Adams
D. H. Adams
Affiliation:
Monash University Clayton, Victoria, Australia
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It is our purpose to show that the constructible orthomodular lattices defined by Janowitz in [2], are embeddable into Boolean lattices. In fact they are subdirect products of Boolean lattices, where the subdirect products are taken in the class of orthomodular posets. We shall make these notions precise. Other concepts, such as disjoint sum and constructible lattice, are defined in [1] and [2].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 3 , May 1973 , pp. 296 - 297
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Janowitz, M. F., ‘The near center of an orthomodular lattice’, J. Aust. Math. Soc.,XIV (1972), 20–29.CrossRefGoogle Scholar
[2]Janowitz, M. F., ‘Constructible Lattices’, J. Aust. Math. Soc.,XIV (1972), 311–316.CrossRefGoogle Scholar
[3]Kochen, S. and Specker, E. P., ‘The problem of hidden variables in quantum mechanics’, J. Math. Mech. 17 (1967), 59–87.Google Scholar
[4]Zeirler, N. and Schlessinger, M., ‘Boolean embedings of orthomodular sets and quantum logic’. Duke Math. J. 32 (1965), 251–262.Google Scholar