Dimension theory in complete orthocomplemented weakly modular lattices

Ramsay, Arlan

doi:10.1090/S0002-9947-1965-0193037-5

Dimension theory in complete orthocomplemented weakly modular lattices
HTML articles powered by AMS MathViewer

by Arlan Ramsay

Trans. Amer. Math. Soc. 116 (1965), 9-31

DOI: https://doi.org/10.1090/S0002-9947-1965-0193037-5

PDF | Request permission

References

Ichiro Amemiya and Israel Halperin, Complemented modular lattices, Canadian J. Math. 11 (1959), 481–520. MR 110655, DOI 10.4153/CJM-1959-047-6
Garrett Birkhoff, Lattice Theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. 25, American Mathematical Society, New York, N. Y., 1948. MR 0029876
R. P. Dilworth, On complemented lattices, Tôhoku Math. J. 47 (1940), 18–23. MR 2843
J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2 (1951), 151–182 (French). MR 48787
D. J. Foulis, Conditions for the modularity of an orthomodular lattice, Pacific J. Math. 11 (1961), 889–895. MR 133270, DOI 10.2140/pjm.1961.11.889
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
Tsurane Iwamura, On continuous geometries. I, Jpn. J. Math. 19 (1944), 57–71. MR 16557, DOI 10.4099/jjm1924.19.1_{5}7
Irving Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math. (2) 61 (1955), 524–541. MR 88476, DOI 10.2307/1969811
L. H. Loomis, The lattice theoretic background of the dimension theory of operator algebras, Mem. Amer. Math. Soc. 18 (1955), 36. MR 73960
George W. Mackey, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155–207. MR 12204, DOI 10.1090/S0002-9947-1945-0012204-1
George W. Mackey, Infinite-dimensional group representations, Bull. Amer. Math. Soc. 69 (1963), 628–686. MR 153784, DOI 10.1090/S0002-9904-1963-10973-8

Horizontal sums of orthocomplemented lattices

10

Atomic orthocomplemented lattices

Fumitomo Maeda, Kontinuierliche Geometrien, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 95, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958 (German). MR 0090579, DOI 10.1007/978-3-642-94727-8
Shûichirô Maeda, Dimension functions on certain general lattices, J. Sci. Hiroshima Univ. Ser. A 19 (1955), 211–237. MR 78338
M. H. Stone, Boundedness properties in function-lattices, Canad. J. Math. 1 (1949), 176–186. MR 29091, DOI 10.4153/cjm-1949-016-5
M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), no. 1, 37–111. MR 1501865, DOI 10.1090/S0002-9947-1936-1501865-8
John von Neumann, Continuous geometry, Princeton Mathematical Series, No. 25, Princeton University Press, Princeton, N.J., 1960. Foreword by Israel Halperin. MR 0120174