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We show that any pseudo MV-algebra is isomorphic with an interval P(G, u), where G is an ^-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of unital £-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 ^-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.2000 Mathematics subject classification: primary 03B50,03G12.

We study pseudo MV-algebras introduced recently by Georgescu and Iorgulescu as a non-commutative generalization of MV-algebras. We introduce a partial binary operation which model the addition in pseudo MValgebras. In the paper, we give basic properties of such an addition. We ®nd conditions which entail the commutativity of pseudo MV-algebras, i.e., when they are classical MValgebras. We study ideals and the conditions when a pseudo MV-algebra is representable. Finally, we introduce states and show how they are connected with the normal ideals.

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