A proof of Whitman’s representation theorem for finite lattices
Author:
S. K. Thomason
Journal:
Proc. Amer. Math. Soc. 25 (1970), 618-619
MSC:
Primary 06.30
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265234-9
MathSciNet review:
0265234
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Abstract | References | Similar Articles | Additional Information
Abstract: The theorem to be proved states that every finite lattice is isomorphic to a sublattice of the lattice $\mathcal {E}(S)$ of all equivalence relations on a countable set $S$. Our proof combines concreteness with freedom from long routine computations.
- Bjarni Jónsson, On the representation of lattices, Math. Scand. 1 (1953), 193–206. MR 58567, DOI https://doi.org/10.7146/math.scand.a-10377
- Philip M. Whitman, Lattices, equivalence relations, and subgroups, Bull. Amer. Math. Soc. 52 (1946), 507–522. MR 16750, DOI https://doi.org/10.1090/S0002-9904-1946-08602-4
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Keywords:
Representations of lattices,
lattices of equivalence relations
Article copyright:
© Copyright 1970
American Mathematical Society