Unital Groups and General Comparability Property

Pseudo-effect algebras are partial algebras (E;+,0,1) with a partially defined addition + which is not necessarily commutative and therefore with two complements, left and right. If they satisfy a special kind of the Riesz decomposition property, they are intervals in unital po-groups. The general comparability property in unital po-groups with strong unit (G,u), allows to compare elements of G in some intervals with Boolean ends. Such a po-group is always an -group admitting a state. We prove that every such (G,u) is a subdirect product of linearly ordered unital po-groups.