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

TL;DR

This paper investigates the Riesz Decomposition Property types of lexicographic products of po-groups and applies these findings to pseudo effect algebras, providing a new representation method using lexicographic products.

Contribution

It introduces a detailed analysis of Riesz Decomposition Properties in lexicographic products and applies these to decompose and represent pseudo effect algebras.

Findings

Characterization of Riesz Decomposition Property types for lexicographic products

Decomposition of pseudo effect algebras into non-void slices

Representation of pseudo effect algebras via lexicographic products

Abstract

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.