The tracial topological rank of extensions of $C^*$-algebras - Hu, Shanwen; Lin, Huaxin; Xue, Yifeng (MATHEMATICA SCANDINAVICA, 2004)
Let $0→ \mathcal J→ \mathcal A→ \mathcal A / \mathcal J→ 0$ be a short exact sequence of separable $C^*$-algebras. We introduce the notion of tracially quasidiagonal extension. Suppose that $\mathcal J$ and $\mathcal A/J$ have tracial topological rank zero. We prove that if $(\mathcal A, \mathcal J)$ is tracially quasidiagonal, then $\mathcal A$ has tracial topological rank zero.