About the Cuntz Comparison for Non-simple C*-algebras

TL;DR

This paper investigates the Cuntz semigroup in non-simple C*-algebras, utilizing the extended Elliott invariant to characterize Cuntz comparison in algebras with the projection property and a single ideal.

Contribution

It introduces a new characterization of Cuntz comparison for a class of non-simple C*-algebras using the extended Elliott invariant.

Findings

Characterization of Cuntz comparison for non-simple C*-algebras with one ideal

Use of the extended Elliott invariant in the analysis

Insights into the structure of C*-algebras with the projection property

Abstract

We study the Cuntz semigroup for non-simple $\text{C}^*$-algebras in this paper. In particular, we use the extended Elliott invariant to characterize the Cuntz comparison for $\text{C}^*$-algebras with the projection property which have only one ideal.