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On generating distributive sublattices of orthomodular lattices. (English) Zbl 0371.06008


MSC:

06D05 Structure and representation theory of distributive lattices
06C15 Complemented lattices, orthocomplemented lattices and posets
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46L10 General theory of von Neumann algebras
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References:

[1] T. S. Blyth and M. F. Janowitz, Residuation theory, Pergamon Press, Oxford-New York-Toronto, Ont., 1972. International Series of Monographs in Pure and Applied Mathematics, Vol. 102. · Zbl 0301.06001
[2] G. D. Crown, A note on distributive sublattices of an orthomodular lattice, J. Natur. Sci. and Math. 16 (1976), no. 1 – 2, 75 – 79. · Zbl 0382.06009
[3] David J. Foulis, A note on orthomodular lattices, Portugal. Math. 21 (1962), 65 – 72. · Zbl 0106.24302
[4] Samuel S. Holland Jr., A Radon-Nikodym theorem in dimension lattices, Trans. Amer. Math. Soc. 108 (1963), 66 – 87. · Zbl 0118.02501
[5] Samuel S. Holland Jr., Distributivity and perspectivity in orthomodular lattices, Trans. Amer. Math. Soc. 112 (1964), 330 – 343. · Zbl 0127.25202
[6] E. L. Marsden, A condition for distribution in orthomodular lattices, Kansas State Univ. Technical Report #23, 1972.
[7] E. L. Marsden and L. M. Herman, A condition for distribution in orthomodular lattices, Kansas State Univ. Technical Report #40, 1974.
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