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A ${{C}^{*}}$ -algebra Ahas the ideal property if any ideal $I$ of $A$ is generated as a closed two-sided ideal by the projections inside the ideal. Suppose that the limit ${{C}^{*}}$ -algebra $A$ of inductive limit of direct sums of matrix algebras over spaces with uniformly bounded dimension has the ideal property. In this paper we will prove that $A$ can be written as an inductive limit of certain very special subhomogeneous algebras, namely, direct sum of dimension-drop interval algebras and matrix algebras over 2-dimensional spaces with torsion ${{H}^{2}}$ groups.

Reduction to Dimension Two of the Local Spectrum for anAHAlgebra with the Ideal Property