Lexicographic Product vs $\mathbb{Q}$-perfect and $\mathbb{H}$-perfect Pseudo Effect Algebras

We study the Riesz Decomposition Property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed to a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.