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Embedding properties of endomorphism semigroups

João Araújo, Friedrich Wehrung (2009)

Fundamenta Mathematicae

Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by Sub V (resp., End V) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply the following: (1) If card Ω ≥ 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff c a r d Γ 2 c a r d Ω . In particular, if Ω has at least two elements, then there exists no semigroup embedding from Self Ω into the dual of PSelf Ω. (2) If V is infinite-dimensional, then...

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