Finite four-generated simple lattices contain all finite lattices
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- by Werner Poguntke and Ivan Rival PDF
- Proc. Amer. Math. Soc. 55 (1976), 22-24 Request permission
Abstract:
Every finite lattice is embeddable in a finite, four-generated, simple lattice.References
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P. Crawley and R. P. Dilworth, Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs, N.J., 1973.
- Richard A. Dean, Component subsets of the free lattice on $n$ generators, Proc. Amer. Math. Soc. 7 (1956), 220โ226. MR 78957, DOI 10.1090/S0002-9939-1956-0078957-4
- Juris Hartmanis, Two embedding theorems for finite lattices, Proc. Amer. Math. Soc. 7 (1956), 571โ577. MR 78960, DOI 10.1090/S0002-9939-1956-0078960-4
- Juris Hartmanis, Lattice theory of generalized partitions, Canadian J. Math. 11 (1959), 97โ106. MR 99931, DOI 10.4153/CJM-1959-013-8
- Yu. I. Sorkin, On the imbedding of latticoids in lattices, Doklady Akad. Nauk SSSR (N.S.) 95 (1954), 931โ934 (Russian). MR 0062099 H. Strietz, Every finite partition lattice is four-generated, Notices Amer. Math. Soc. 22 (1975), A-507.
- Philip M. Whitman, Lattices, equivalence relations, and subgroups, Bull. Amer. Math. Soc. 52 (1946), 507โ522. MR 16750, DOI 10.1090/S0002-9904-1946-08602-4
- R. Wille, A note on simple lattices, Lattice theory (Proc. Colloq., Szeged, 1974) Colloq. Math. Soc. Jรกnos Bolyai, Vol. 14, North-Holland, Amsterdam, 1976, pp.ย 455โ462. MR 0434903
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 22-24
- DOI: https://doi.org/10.1090/S0002-9939-1976-0392717-9
- MathSciNet review: 0392717