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