Lexicographic product vs $$\mathbb Q$$Q-perfect and $$\mathbb H$$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 into a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.