Unitizations of generalized pseudo effect algebras and their ideals

TL;DR

This paper investigates how generalized pseudo effect algebras can be embedded into larger structures with units using automorphisms, focusing on congruences and ideals.

Contribution

It introduces the concept of unitizations of GPEAs via automorphisms and analyzes their properties, especially regarding congruences and ideals.

Findings

GPEAs can be embedded into unitized structures with a unit.

Automorphisms play a key role in the unitization process.

The behavior of congruences and ideals is characterized in the unitized setting.

Abstract

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphism, paying special attention to the behavior of congruences and ideals in this setting.