  We give a complete classification of the ideals of the core of the
C*-algebras associated with self-similar maps under a certain condition. Any
ideal is completely determined by the intersection with the coefficient algebra
C(K) of the self-similar set K. The corresponding closed subset of K is
described by the singularity structure of the self-similar map. In particular
the core is simple if and only if the self-similar map has no branch point. A
matrix representation of the core is essentially used to prove the
classification.
