TY - JOUR
T1 - Universality of the lattice of transformation monoids
AU - Pinsker, Michael
AU - Shelah, Saharon
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Algebraic lattice
KW - Closed sublattice
KW - Submonoid
KW - Transformation monoid
UR - http://www.scopus.com/inward/record.url?scp=84879302262&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2013-11566-2
DO - 10.1090/S0002-9939-2013-11566-2
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AN - SCOPUS:84879302262
SN - 0002-9939
VL - 141
SP - 3005
EP - 3011
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -