A short return to simple AH-algebras with real rank zero

Abstract

Let $A$ be a unital simple AH-algebra with stable rank one and real rank zero such that $kx=0$ for all $x\in \ker {\rho }_A,$ the subgroup of infinitesmal elements in $K_0(A),$ and for the same integer $k\ge 1.$ We show that $A$ has tracial rank zero and is isomorphic to a unital simple AH-algebra with no dimension growth.

References in corpus (1)

• Approximate Homotopy of Homomorphisms from $C(X)$ into a Simple $C^{\ast }$-algebra