Compressing coefficients while preserving ideals in K-theory for C*-algebras

An invariant based on ordered K-theory with coefficients in Z + +(n>1) Z/n and an infinite number of natural transformations has proved to be necessary and sufficient to classify a large class of nonsimple C*-algebras. In this paper, we expose and explain the relations between the order structure and the ideals of the C*-algebras in question. As an application, we give a new complete invariant for a large class of approximately subhomogeneous C*-algebras. The invariant is based on ordered K-theory with coefficients in Z+Q+Q/Z. This invariant is more compact thence, easier to compute) than the invariant mentioned above, and its use requires computation of only four natural transformations.