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  • Pseudo MV-algebras are intervals in ℓ-groups

  • Part of
  • Anatolij Dvurečenskij
  • Journal:
    Journal of the Australian Mathematical Society / Volume 72 / Issue 3 / June 2002
    Published online by Cambridge University Press:
    09 April 2009, pp. 427-446
    Print publication:
    June 2002
    • Article
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  • We show that any pseudo MV-algebra is isomorphic with an interval Γ(G, u), where G is an ℓ-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of unital ℓ-groups is categorically equivalent with the category of pseudo MV-algebras. Since pseudo MV-algebras are a non-commutative generalization of MV-algebras, our assertions generalize a famous result of Mundici for a representation of MV-algebras by Abelian unital ℓ-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.