MV-algebras and Partially Cyclically Ordered Groups

We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are the wound-rounds of lattice-ordered groups. It follows some results about can be stated in terms MV-algebras. For example, study together with cyclic order allows to get first-order characterization unimodular complex numbers finite deduce pseudofinite MV-chains pseudo-simple (i.e. share same properties as simple ones). generalize these non-linearly MV-algebras, for example hyperarchimedean