Representation of perfect and n-perfect pseudo effect algebras

A perfect (an n-perfect) pseudo effect algebra can be decomposed into two (n + 1 many) non-empty and mutually comparable slices. They generalize perfect MV-algebras studied in [5]. We characterize such a pseudo effect algebra as an interval in the semidirect product of the po-group Z or n1 Z with a directed po-group G satisfying a stronger type of the Riesz Decomposition Property, RDP1, and the semidirect product is ordered lexicographically. We show that the category of perfect and the category of n-perfect pseudo effect algebras with RDP1 are categorically equivalent to a special category of directed po-groups satisfying RDP1.(c) 2022 Elsevier B.V. All rights reserved.