Journal of Science of the Hiroshima University, Series A-I (Mathematics)

Dimension theory on relatively semi-orthocomplemented complete lattices

Shûichirô Maeda

Full-text: Open access

Article information

Source
J. Sci. Hiroshima Univ. Ser. A-I Math., Volume 25, Number 2 (1961), 369-404.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206139804

Digital Object Identifier
doi:10.32917/hmj/1206139804

Mathematical Reviews number (MathSciNet)
MR0150069

Zentralblatt MATH identifier
0104.25703

Subjects
Primary: 06.40

Citation

Maeda, Shûichirô. Dimension theory on relatively semi-orthocomplemented complete lattices. J. Sci. Hiroshima Univ. Ser. A-I Math. 25 (1961), no. 2, 369--404. doi:10.32917/hmj/1206139804. https://projecteuclid.org/euclid.hmj/1206139804


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References

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  • [2] S. K.Berberian, On the projection geometry of a finite AW*-algebra, Trans. Amer. Math. Soc, 83 (1956), 493-509.
  • [3] J. Dixmier, Les algebres d'operateurs dans espace hilbertien, Paris, 1957.
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  • [5] I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235-249.
  • [6] I. Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math., 61 (1955), 524-541.
  • [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).
  • [9] F. Maeda, Kontinuierliche Geometrien, Berlin, 1958.
  • [10] F. Maeda, Kontinuierliche Geometrien, Decompositions of general lattices into direct summands of types I, II and III, this Journal, 23 (1959), 151-170.
  • [ll] S. Maeda, Dimension functions on certain general lattices, ibid., 19 (1955), 211-237.
  • [12] S. Maeda, On the lattice of projections of a Baer *-ring, ibid., 22 (1958), 75-88.
  • [13] S. Maeda, On relatively semi-orthocomplemented lattices, idid., 24 (1960), 155-161.
  • [14] S. Maeda, On a ring whose principal right ideals generated by idempotents form a lattice, ibid., 24 (1960), 509-525.
  • [15] J. von Neumann, Continuous geometry, Princeton, 1960.