Segments of ordered sets
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- by W. D. Duthie
- Trans. Amer. Math. Soc. 51 (1942), 1-14
- DOI: https://doi.org/10.1090/S0002-9947-1942-0007032-4
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References
- G. Birkhoff, On combinations of subalgebras, Proceedings of the Cambridge Philosophical Society, vol. 29 (1933), pp. 441-464.
- Garrett Birkhoff, Lattice Theory, American Mathematical Society, New York, 1940. MR 0001959
- Oystein Ore, On the foundation of abstract algebra. I, Ann. of Math. (2) 36 (1935), no. 2, 406–437. MR 1503232, DOI 10.2307/1968580
- M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), no. 1, 37–111. MR 1501865, DOI 10.1090/S0002-9947-1936-1501865-8 —, Topological representations of distributive lattices and Brouwerian logics, Časopis pro Pěstovāní Matematiky a Fysiky, vol. 67 (1937), pp. 1-25. J. von Neumann, Continuous Geometry, vols. 1, 2, Planographed Princeton Mathematical Notes.
- Morgan Ward, A characterization of Dedekind structures, Bull. Amer. Math. Soc. 45 (1939), no. 6, 448–451. MR 1564002, DOI 10.1090/S0002-9904-1939-07005-5
- L. R. Wilcox, Modularity in the theory of lattices, Ann. of Math. (2) 40 (1939), no. 2, 490–505. MR 1503473, DOI 10.2307/1968934 W. D. Duthie, Segments in ordered sets, doctoral thesis, Princeton University, 1940.
Bibliographic Information
- © Copyright 1942 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 51 (1942), 1-14
- MSC: Primary 27.2X
- DOI: https://doi.org/10.1090/S0002-9947-1942-0007032-4
- MathSciNet review: 0007032