On generating distributive sublattices of orthomodular lattices
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- by Richard J. Greechie PDF
- Proc. Amer. Math. Soc. 67 (1977), 17-22 Request permission
Addendum: Proc. Amer. Math. Soc. 76 (1979), 216-218.
Abstract:
A Foulis-Holland set is a nonempty subset S of an orthomodular lattice such that whenever x, y, z are distinct elements of S one of them commutes with the other two. If S is a Foulis-Holland set, then the sublattice generated by S is distributive.References
- T. S. Blyth and M. F. Janowitz, Residuation theory, International Series of Monographs in Pure and Applied Mathematics, Vol. 102, Pergamon Press, Oxford-New York-Toronto, Ont., 1972. MR 0396359
- G. D. Crown, A note on distributive sublattices of an orthomodular lattice, J. Nat. Sci. and Math. 16 (1976), no. 1-2, 75–79. MR 463061, DOI 10.1080/03081088208817474
- David J. Foulis, A note on orthomodular lattices, Portugal. Math. 21 (1962), 65–72. MR 148581
- Samuel S. Holland Jr., A Radon-Nikodym theorem in dimension lattices, Trans. Amer. Math. Soc. 108 (1963), 66–87. MR 151407, DOI 10.1090/S0002-9947-1963-0151407-3
- Samuel S. Holland Jr., Distributivity and perspectivity in orthomodular lattices, Trans. Amer. Math. Soc. 112 (1964), 330–343. MR 168498, DOI 10.1090/S0002-9947-1964-0168498-7 E. L. Marsden, A condition for distribution in orthomodular lattices, Kansas State Univ. Technical Report #23, 1972. E. L. Marsden and L. M. Herman, A condition for distribution in orthomodular lattices, Kansas State Univ. Technical Report #40, 1974.
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 67 (1977), 17-22
- MSC: Primary 06A30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0450157-9
- MathSciNet review: 0450157