n-Perfect and $\mathbb{Q}$-Perfect Pseudo Effect Algebras.

An n-perfect pseudo effect algebra means that it can be decomposed into n+1 comparable slices. We show that such a pseudo effect algebra satisfying a Riesz Decomposition Property type corresponds to the lexicographic product of a cyclic group $\frac{1}{n}\mathbb{Z}$ with some po-group. The analogous result will be proved for strong $\mathbb{Q}$-perfect pseudo effect algebras. [ABSTRACT FROM AUTHOR]