Building Modules From the Singular Locus

  • Jesse Burke
  • Lars Winther Christensen
  • Ryo Takahashi


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.
How to Cite
Burke, J., Christensen, L. W., & Takahashi, R. (2015). Building Modules From the Singular Locus. MATHEMATICA SCANDINAVICA, 116(1), 23-33.