  A finitely generated module over a commutative noetherian ring of finite
Krull dimension can be built from the prime ideals in the singular locus by
iteration of three procedures: taking extensions, direct summands, and
cosyzygies. In 2003 Schoutens gave a bound on the number of iterations required
to build any module, and in this note we determine the exact number. This
building process yields a stratification of the module category, which we study
in detail for local rings that have an isolated singularity.
