On modular lattices of order dimension two
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- by Rudolf Wille PDF
- Proc. Amer. Math. Soc. 43 (1974), 287-292 Request permission
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
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K. A. Baker, Dimension, join-independence, and breadth in partially ordered sets, Honors Thesis, Harvard University, Cambridge, Mass., 1961.
- K. A. Baker, P. C. Fishburn, and F. S. Roberts, Partial orders of dimension $2$, Networks 2 (1972), 11–28. MR 300944, DOI 10.1002/net.3230020103
- Ben Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941), 600–610. MR 4862, DOI 10.2307/2371374
- Egbert Harzheim, Ein Endlichkeitssatz über die Dimension teilweise geordneter Mengen, Math. Nachr. 46 (1970), 183–188 (German). MR 274348, DOI 10.1002/mana.19700460115
Additional Information
- © Copyright 1974 American Mathematical Society
- 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