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Transactions of the American Mathematical Society

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Dimension theory in complete orthocomplemented weakly modular lattices


Author: Arlan Ramsay
Journal: Trans. Amer. Math. Soc. 116 (1965), 9-31
MSC: Primary 06.40
DOI: https://doi.org/10.1090/S0002-9947-1965-0193037-5
MathSciNet review: 0193037
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  • [1] I. Amemiya and I. Halperin, Complemented modular lattices, Canad. J. Math. 11 (1959), 481-520. MR 0110655 (22:1530)
  • [2] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. Vol. 25, Amer. Math. Soc., Providence, R. I., 1948. MR 0029876 (10:673a)
  • [3] R. P. Dilworth, On complemented lattices, Tôhoku Math. J. 47 (1940), 18-23. MR 0002843 (2:120d)
  • [4] J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2 (1951), 151-182. MR 0048787 (14:69e)
  • [5] D. J. Foulis, Conditions for the modularity of an orthomodular lattice, Pacific J. Math. 11 (1961), 889-895. MR 0133270 (24:A3104)
  • [6] S. S. Holland, Jr., Distributivity and perspectivity in orthomodular lattices, Trans. Amer. Math. Soc. 112 (1964), 330-343. MR 0168498 (29:5760)
  • [7] T. Iwamura, On continuous geometries. I, Japan. J. Math. 9 (1944), 57-71. MR 0016557 (8:35b)
  • [8] I. Kaplansky, Any complete orthocomplemented modular lattice is a continuous geometry, Ann. of Math. (2) 61 (1955), 524-541. MR 0088476 (19:524f)
  • [9] L. H. Loomis, The lattice theoretic background of the dimension theory of operator algebras, Mem. Amer. Math. Soc. No. 18 (1955), 36 pp. MR 0073960 (17:514f)
  • [10] G. W. Mackey, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155-207. MR 0012204 (6:274d)
  • [11] -, Infinite-dimensional group representations, Bull. Amer. Math. Soc. 69 (1963), 628-686. MR 0153784 (27:3745)
  • [12] M. D. MacLaren, Horizontal sums of orthocomplemented lattices, Notices Amer. Math. Soc. 10 (1963), 63.
  • [13] -, Atomic orthocomplemented lattices, Math. Note No. 286, Boeing Scientific Research Laboratories, Seattle, Washington, 1963.
  • [14] F. Maeda, Kontinuierliche Geometrien, Springer-Verlag, Berlin, 1958. MR 0090579 (19:833c)
  • [15] S. Maeda, Dimension functions on certain general lattices, J. Sci. Hiroshima Univ. Ser. A-I Math. 19 (1955), 211-237. MR 0078338 (17:1177d)
  • [16] M. H. Stone, Boundedness properties in function-lattices, Canad. J. Math. 1 (1949), 176-186. MR 0029091 (10:546a)
  • [17] -, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), 37-111. MR 1501865
  • [18] J. von Neumann, Continuous geometry, Princeton Univ. Press, Princeton, N. J., 1960. MR 0120174 (22:10931)

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DOI: https://doi.org/10.1090/S0002-9947-1965-0193037-5
Article copyright: © Copyright 1965 American Mathematical Society

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