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Orthogonality relations and orthomodularity

Published online by Cambridge University Press:  17 April 2009

P.D. Finch
P.D. Finch
Affiliation:
Monash University, Clayton, Victoria.
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Abstract

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An abstract orthogonality relation is defined, a closure operation and a corresponding lattice of closed sets are associated with it. Necessary and sufficient conditions are obtained for the orthomodularity of a sub-ortholattice of the lattice of closed sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 1 , February 1970 , pp. 125 - 128
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Birkhoff, Garrett, Lattice theory (Colloquium Publ. 25, Amer. Math. Soc., Providence, 3rd ed., 1967).Google Scholar
[2]Finch, P.D., “On orthomodular posets”, J. Austral. Math. Soc. (to appear).Google Scholar
[3]MacLaren, M. Donald, “Atomic ortbocomplemented lattices”, Pacific J. Math. 14 (1964), 597–612.CrossRefGoogle Scholar