Pacific Journal of Mathematics

Partition and modulated lattices.

David Sachs

Article information

Source
Pacific J. Math., Volume 11, Number 1 (1961), 325-345.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103037557

Mathematical Reviews number (MathSciNet)
MR0122742

Zentralblatt MATH identifier
0238.06007

Subjects
Primary: 06.40

Citation

Sachs, David. Partition and modulated lattices. Pacific J. Math. 11 (1961), no. 1, 325--345. https://projecteuclid.org/euclid.pjm/1103037557


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References

  • [1] Garrett Birkhoff, Lattice Theory, Rev. Ed. New York: Amer. Math. Soc, 1948.
  • [2] R. P. Dilworth, The structure of relatively complemented lattices, Ann. of Math., 51 (1950), 348-59.
  • [3] M. L. Dubreil-Jacotin, L. Lesieur and R. Croisot, Leons sur la Theorie Des Treillis Des StructuresAlgebriques Ordonnees et Des Treillis Gometriques. Paris: Gauthier-Villars, 1953.
  • [4] J. E. McLaughlin, Projectivities in relatively complemented lattices, Duke Math. J., 18 (1951), 73-84.
  • [5] J. E. McLaughlin, Structuretheorems for relatively complemented lattices, Pacific J. Math., 3 {1953), 197-208.
  • [6] O. Ore, Theory of equivalence relations, Duke Math. J., 9 (1942), 573-627.
  • [7] U. Sasaki and S. Fujiwara, The decomposition of matroid lattices, J. Sci. Hiroshima Univ. Ser. A., 15 (1952), 183-88. S., The characterization of partition lattices J. Sci. Hiroshima Univ. Ser. A., 15 (1952), 189-201.
  • [9] L. R. Wilcox and M. F. Smiley, Metric lattices, Ann. of Math., 40 (1939), 309-27, corrected ibid., 47 (1946), 831.
  • [10] L. R. Wilcox and M. F. Smiley, A Note on complementation in lattices, Bull. Amer. Math. Soc, 48 (1942), 453-58.