Boolean Skeletons of MV-algebras and ℓ-groups

Studia Logica 98 (1-2):141-147 (2011)
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
Keywords MV-algebras  lattice-ordered abelian groups   ℓ-ideals  direct decompositions  Boolean products
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