Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-09T09:18:28.474Z Has data issue: false hasContentIssue false
  • English
  • Français

Congruence relations on orthomodular lattices

Published online by Cambridge University Press:  09 April 2009

P. D. Finch
P. D. Finch
Affiliation:
Monash UniversityMelbourne
Rights & Permissions [Opens in a new window]

Extract

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.

We denote lattice join and meet by ∨ and ∧ respectively and the associated partial order by ≧. A lattice L with 0 and I is said to be orthocomplemented if it admits a dual automorphism x → x′, that is a one-one mapping of L onto itself such that which is involutive, so that for each x in L and, further, is such that for each x in L.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1966 , pp. 46 - 54
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Birkhoff, G., Lattice Theory, Revised edition, Amer. Math. Soc. Coll. Publ., Vol. 25, New York, 1948.Google Scholar
[2]Finch, P. D., Probability on orthomodular lattices (submitted for publication in this Journal).Google Scholar
[3]Halmos, P. R., Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea, New York 1957.Google Scholar
[4]Mackey, G. W., Mathematical foundations of quantum mechanics, Benjamin Inc, New York, 1963.Google Scholar
[5]von Neumann, J., Functional operators, Vol. 2, Princeton, 1950.Google Scholar