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On modular lattices of order dimension two


Author: Rudolf Wille
Journal: Proc. Amer. Math. Soc. 43 (1974), 287-292
MSC: Primary 06A30
DOI: https://doi.org/10.1090/S0002-9939-1974-0329988-9
MathSciNet review: 0329988
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Abstract: In this note, it is shown that a modular lattice has order dimension $ \leqq 2$ if and only if it contains no subset isomorphic to one of five described partially ordered sets.


References [Enhancements On Off] (What's this?)

  • [1] K. A. Baker, Dimension, join-independence, and breadth in partially ordered sets, Honors Thesis, Harvard University, Cambridge, Mass., 1961.
  • [2] K. A. Baker, P. C. Fishburn and F. S. Roberts, Partial orders of dimension 2, interval orders, and interval graphs, Mimeographed, Rand Corporation, 1970. MR 0300944 (46:104)
  • [3] B. Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941), 600-610. MR 3, 73. MR 0004862 (3:73a)
  • [4] E. Harzheim, Ein Endlichkeitssatz über die Dimension teilweise geordneter Mengen, Math. Nachr. 46 (1970), 183-188. MR 43 #113. MR 0274348 (43:113)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0329988-9
Keywords: Partially ordered set, order dimension, lattice, modular, distributive, finitely generated
Article copyright: © Copyright 1974 American Mathematical Society

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