# Nuclear dimension of simple stably projectionless C*-algebras

## TL;DR

This paper proves that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1, establishing a key equivalence in the classification theory of these algebras.

## Contribution

It demonstrates that Z-stability implies nuclear dimension at most 1 for a broad class of C*-algebras, completing a fundamental equivalence in the field.

## Key findings

- Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension ≤ 1
- Completes the equivalence between finite nuclear dimension and Z-stability
- Advances classification program for non-elementary C*-algebras

## Abstract

We prove that Z-stable, simple, separable, nuclear, non-unital C*-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and Z-stability for simple, separable, nuclear, non-elementary C*-algebras.