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Lifts for semigroups of monomorphisms of an independence algebra

João Araújo — 2003

Colloquium Mathematicae

For a universal algebra 𝓐, let End(𝓐) and Aut(𝓐) denote, respectively, the endomorphism monoid and the automorphism group of 𝓐. Let S be a semigroup and let T be a characteristic subsemigroup of S. We say that ϕ ∈ Aut(S) is a lift for ψ ∈ Aut(T) if ϕ|T = ψ. For ψ ∈ Aut(T) we denote by L(ψ) the set of lifts of ψ, that is, L(ψ) = {ϕ ∈ Aut(S) | ϕ|T = ψ}. Let 𝓐 be an independence algebra of infinite rank and let S be a monoid of monomorphisms such that G = Aut(𝓐) ≤ S ≤ End(𝓐). In [2] it is proved...

Lifts for semigroups of endomorphisms of an independence algebra

João Araújo — 2006

Colloquium Mathematicae

For a universal algebra , let End() and Aut() denote, respectively, the endomorphism monoid and the automorphism group of . Let S be a semigroup and let T be a characteristic subsemigroup of S. We say that ϕ ∈ Aut(S) is a lift for ψ ∈ Aut(T) if ϕ|T = ψ. For ψ ∈ Aut(T) we denote by L(ψ) the set of lifts of ψ, that is, L ( ψ ) = ϕ A u t ( S ) | ϕ | T = ψ . Let be an independence algebra of infinite rank and let S be a monoid of monomorphisms such that G = Aut() ≤ S ≤ End(). It is obvious that G is characteristic in S....

Embedding properties of endomorphism semigroups

João AraújoFriedrich 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...

Independent axiom systems for nearlattices

João AraújoMichael Kinyon — 2011

Czechoslovak Mathematical Journal

A nearlattice is a join semilattice such that every principal filter is a lattice with respect to the induced order. Hickman and later Chajda et al independently showed that nearlattices can be treated as varieties of algebras with a ternary operation satisfying certain axioms. Our main result is that the variety of nearlattices is 2 -based, and we exhibit an explicit system of two independent identities. We also show that the original axiom systems of Hickman as well as that of Chajda et al are...

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