Lifts for semigroups of monomorphisms of an independence algebra

• Autorzy: João Araújo
• Języki publikacji: EN

Abstrakty

EN

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 that if 𝓐 is a set (that is, an algebra without operations), then |L(ϕ)| = 1. The analogous result for vector spaces does not hold. Thus the natural question is: Characterize the independence algebras in which |L(ϕ)| = 1. The aim of this note is to answer this question.

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.
• 20M10: General structure theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 97
• Numer: 2
• Strony: 277-284

Daty

wydano

2003

Twórcy

autor

João Araújo

• Universidade Aberta, R. Escola Politécnica, 147, 1269-001 Lisboa, Portugal
• Centro de Álgebra, Universidade de Lisboa, Av. Gama Pinto, 2, 1649-003 Lisboa, Portugal

Identyfikatory

DOI

10.4064/cm97-2-11