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

On the symmetry of the modular relation in atomic lattices

Shûichirô Maeda

Full-text: Open access

Article information

Source
J. Sci. Hiroshima Univ. Ser. A-I Math. Volume 29, Number 2 (1965), 165-170.

Dates
First available: 21 March 2008

Permanent link to this document
http://projecteuclid.org/euclid.hmj/1206139232

Mathematical Reviews number (MathSciNet)
MR0191854

Zentralblatt MATH identifier
0146.01603

Subjects
Primary: 06.40

Citation

Maeda, Shûichirô. On the symmetry of the modular relation in atomic lattices. Journal of Science of the Hiroshima University, Series A-I (Mathematics) 29 (1965), no. 2, 165--170. http://projecteuclid.org/euclid.hmj/1206139232.


Export citation

References

  • [1] G. Birkhoff, Lattice theory,New York, 1948.
  • [2] M. L. Dubreil-Jacotin, L. Lesieur and R. Croisot, Leons sur la thorie des treillis des structures algebriques ordonnees et des treillis geometriques, Paris, 1953.
  • [3] I. Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math., 61 (1955),524-541.
  • [4] M. D. MacLaren, Atomic orthocomplemented lattices, Pacific J. Math., 14 (1964),597-612.
  • [5] F. Maeda, Matroid lattices of infinite length, this Journal, 15 (1952), 177-182.
  • [6] F. Maeda, Perspectivity of points in matroidlattices, ibid., 28 (1964),101-112.
  • [7] G. Piron, Axiomatique quantique, Helv. Phys. Acta, 37 (1964),439-468.
  • [8] D. Sachs, Partition and modulated lattices, Pacific J. Math., 11 (1961),325-345.
  • [9] U. Sasaki, Semi-modularity in relatively atomic,upper continuous lattices, this Journal, 16 (1953),409- 416.
  • [10] L. R. Wilcox, Modularity in the theory of lattices, Ann. of Math., 40 (1939),490-505.