A Complete Invariant forADAlgebras with Real Rank Zero and Bounded Torsion inK1

For each integerp>1, we consider an algebraic invariant forC*-algebras. The invariant consists ofK0,K1, theK0-group with Z/pcoefficients, the order structures these groups possess, and the natural maps between the three groups. We prove that this invariant is complete for the class ofADalgebras of real rank zero ifpannihilates every torsion element ofK1. TheADalgebras areC*-algebras which are inductive limits of finite direct sums ofC*-algebras of continuous matrix-valued functions over the circle, or over the interval, where in the interval case we require that the value over the endpoints is a scalar multiple of the unit matrix. Examples show that the condition on the torsion inK1is necessary when only one modp K0-group is considered. Applying a theorem of Dădărlat, the result also applies to a subclass of theAHalgebras.