The Lexicographic Product of Po-groups and n-Perfect Pseudo Effect Algebras

We study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. Special attention is paid to the lexicographic product of the group of integers with an arbitrary po-group. Then we apply these results to the study of n-perfect pseudo effect algebras. We show that the category of strong n-perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups with RDP1.