Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-29T00:02:15.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Orthogonality relations and orthomodularity

Published online by Cambridge University Press:  17 April 2009

P.D. Finch
P.D. Finch
Affiliation:
Monash University, Clayton, Victoria.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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