Nuclear dimension of simple stably projectionless $\mathrm{C}^*$-algebras

Abstract

We prove that $\mathcal{𝒵}$-stable, simple, separable, nuclear, nonunital $C^{\ast }$-algebras have nuclear dimension at most 1. This completes the equivalence between finite nuclear dimension and $\mathcal{𝒵}$-stability for simple, separable, nuclear, nonelementary $C^{\ast }$-algebras.