Andrew S. Toms, Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907, USA; e-mail: atoms@purdue.edu

We observe almost divisibility for the original Cuntz semigroup of a simple AH algebra with strict comparison. As a consequence, the properties of strict comparison, finite nuclear dimension, and \(\mathcal{Z}\)-stability are equivalent for such algebras, confirming partially a conjecture of Winter and the author.

\(\mathcal{Z}\)-stabilité sont équivalentes pour une telle algèbre, ce qui confirme partiellement une conjecture de Winter et de l’auteur.