Kite $n$-Perfect Pseudo Effect Algebras

TL;DR

This paper introduces a new class of kite pseudo effect algebras, provides their representation via lexicographic extensions, and characterizes their subdirectly irreducible components, advancing the algebraic theory.

Contribution

It offers a novel representation for kite pseudo effect algebras and introduces kite n-perfect pseudo effect algebras with a characterization of their irreducible forms.

Findings

Representation of kite pseudo effect algebras as intervals in lexicographic extensions.

Introduction of kite n-perfect pseudo effect algebras.

Characterization of subdirectly irreducible kite algebras.

Abstract

Kite pseudo effect algebras were recently introduced as a class of interesting examples of pseudo effect algebras using a po-group, an index set and two bijections on the index set. We represent kite pseudo effect algebras with a special kind of the Riesz decomposition property as an interval in a lexicographic extension of the po-group which solves an open problem on representation of kites. In addition, we introduce kite $n$-perfect pseudo effect algebras and we characterize subdirectly irreducible algebras which are building stones of the theory.