Dimension theory on relatively semi-orthocomplemented complete lattices
Shûichirô Maeda
Source: J. Sci. Hiroshima Univ. Ser. A-I Math. Volume 25, Number 2
(1961), 369-404.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206139804
Mathematical Reviews number (MathSciNet): MR0150069
Zentralblatt MATH identifier: 0104.25703
References
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[3] J. Dixmier, Les algebres d'operateurs dans espace hilbertien, Paris, 1957.
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[4] I Halperin, Dimensionality in reducible geometries, Ann. of Math., 40 (1939), 581-599.
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[5] I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235-249.
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[6] I. Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math., 61 (1955), 524-541.
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[7] I. Kaplansky, Rings of operators, University of Chicago mimeographed notes, 1955.
[8] L. H. Loomis, The lattice theoretic background of the dimension theory of operator algebras, Memoirs of Amer. Math. Soc, 18 (1955).
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[9] F. Maeda, Kontinuierliche Geometrien, Berlin, 1958.
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[10] F. Maeda, Kontinuierliche Geometrien, Decompositions of general lattices into direct summands of types I, II and III, this Journal, 23 (1959), 151-170.
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[ll] S. Maeda, Dimension functions on certain general lattices, ibid., 19 (1955), 211-237.
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[12] S. Maeda, On the lattice of projections of a Baer *-ring, ibid., 22 (1958), 75-88.
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[13] S. Maeda, On relatively semi-orthocomplemented lattices, idid., 24 (1960), 155-161.
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[14] S. Maeda, On a ring whose principal right ideals generated by idempotents form a lattice, ibid., 24 (1960), 509-525.
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[15] J. von Neumann, Continuous geometry, Princeton, 1960.
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Journal of Science of the Hiroshima University, Series A-I (Mathematics)
