Abstract
Let Γ be Mundici’s functor from the category \({\mathcal{LG}}\) whose objects are the lattice-ordered abelian groups (ℓ-groups for short) with a distinguished strong order unit and the morphisms are the unital homomorphisms, onto the category \({\mathcal{MV}}\) of MV-algebras and homomorphisms. It is shown that for each strong order unit u of an ℓ-group G, the Boolean skeleton of the MV-algebra Γ(G, u) is isomorphic to the Boolean algebra of factor congruences of G.
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Cignoli, R. Boolean Skeletons of MV-algebras and ℓ-groups. Stud Logica 98, 141–147 (2011). https://doi.org/10.1007/s11225-011-9325-3
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DOI: https://doi.org/10.1007/s11225-011-9325-3