Embedding coproducts of partition lattices

Details Embedding coproducts of partition lattices Embedding coproducts of partition lattices

2007-09-27

arxiv.org/abs/0709.4469v2

Mathematics

Rings and Algebras

To appear in Acta Sci. Math. (Szeged)

Scientific paper

We prove that the lattice Eq(X) of all equivalence relations on an infinite
set X contains, as a 0,1-sublattice, the 0-coproduct of two copies of itself,
thus answering a question by G.M. Bergman. Hence, by using methods initiated by
de Bruijn and further developed by Bergman, we obtain that Eq(X) also contains,
as a sublattice, the coproduct of 2^{card(X)} copies of itself.

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