Embedding coproducts of partition lattices

2007/09/27 by Friedrich Wehrung, Wehrung, Friedrich
Mathematics · #06B10 #06B15 (Primary) #06B25 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B10 #msc:06B15 #msc:06B25

paper · pdf · doi:10.48550/arxiv.0709.4469

To appear in Acta Sci. Math. (Szeged)

arxiv created 2007/10/15 · arxiv updated 2009/12/01

Abstract

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.

Related

• Algebraic lattices are complete sublattices of the clone lattice over an infinite set
• Partitions and their lattices
• Enumerating lattices of subsets
• Dedekind's Transposition Principle for lattices of equivalence relations
• Bounds on the cardinality of partition