Embedding coproducts of partition lattices

Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Lattice; equivalence relation; embedding; coproduct; ideal; filter; upper continuous

Domaines: Anneaux et algèbres [math.RA]; Mathématiques générales [math.GM]

Friedrich Wehrung. Embedding coproducts of partition lattices. Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum, 2007, 73, pp.429--443. ⟨hal-00175368v2⟩