Universality of the lattice of transformation monoids

Michael Pinsker; Saharon Shelah

doi:10.1090/S0002-9939-2013-11566-2

Universality of the lattice of transformation monoids

Michael Pinsker
, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 2^λ 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 2^λ compact elements.

Original language	English
Pages (from-to)	3005-3011
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	9
DOIs	https://doi.org/10.1090/S0002-9939-2013-11566-2
State	Published - 2013

Keywords

Algebraic lattice
Closed sublattice
Submonoid
Transformation monoid

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10.1090/S0002-9939-2013-11566-2

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Universality of the lattice of transformation monoids

Abstract

Keywords

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