J. Austral. Math. Soc.  72 (2002), 427-445
Pseudo MV-algebras are intervals in $\ell$-groups

Anatolij Dvurecenskij
  Mathematical Institute
  Slovak Academy of Sciences
  Stefánikova 49
  SK-814 73 Bratislava

We show that any pseudo MV-algebra is isomorphic with an interval $\Gamma(G,u)$, where $G$ is an $\ell$-group not necessarily Abelian with a strong unit $u$. In addition, we prove that the category of unital $\ell$-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 $\ell$-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.
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