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

Let $A$ be a unital simple AH-algebra with stable rank one and real rank zero such that $kx=0$ for all $x\in {\rm ker}ρ_A,$ 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.

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