On pseudo MV-algebras

 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 MV-algebras. In the paper, we give basic properties of such an addition. We find conditions which entail the commutativity of pseudo MV-algebras, i.e., when they are classical MV-algebras. 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.