On automorphisms of algebras with a single unary operation

Fuhrken, G.

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Nonlinearity of the automorphism groups of some free algebras.

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Tame Automorphisms of ℂ³ with Multidegree of the Form (p₁,p₂,d₃)

Marek Karaś (2011)

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Let d₃ ≥ p₂ > p₁ ≥ 3 be integers such that p₁,p₂ are prime numbers. We show that the sequence (p₁,p₂,d₃) is the multidegree of some tame automorphism of ℂ³ if and only if d₃ ∈ p₁ℕ + p₂ℕ, i.e. if and only if d₃ is a linear combination of p₁ and p₂ with coefficients in ℕ.

A finiteness condition on automorphism groups

Federico Menegazzo, Derek J. S. Robinson (1987)

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Lifts for semigroups of monomorphisms of an independence algebra

João Araújo (2003)

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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...