Universality of the lattice of transformation monoids

Michael Pinsker, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The set of all transformation monoids on a fixed set of infinite cardinality λ, equipped with the order of inclusion, forms a complete algebraic lattice Mon(λ) with 2λ compact elements. We show that this lattice is universal with respect to closed sublattices; i.e., the closed sublattices of Mon(λ) are, up to isomorphism, precisely the complete algebraic lattices with at most 2λ compact elements.

Original languageEnglish
Pages (from-to)3005-3011
Number of pages7
JournalProceedings of the American Mathematical Society
Volume141
Issue number9
DOIs
StatePublished - 2013

Keywords

  • Algebraic lattice
  • Closed sublattice
  • Submonoid
  • Transformation monoid

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