Kite Pseudo Effect Algebras

TL;DR

This paper introduces kite pseudo effect algebras, a new class linked to partially ordered groups, allowing for noncommutative structures and exploring their properties and conditions for minimal ideals.

Contribution

It defines kite pseudo effect algebras, connecting them with po-groups and Riesz Decomposition Properties, and analyzes their ideal structure.

Findings

Kite pseudo effect algebras can be noncommutative even from Abelian po-groups.

They are related to different Riesz Decomposition Properties.

Conditions for the existence of the least non-trivial normal ideal are established.

Abstract

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least non-trivial normal ideal.