Cohen–Macaulay Modules of Infinite Projective Dimension

Abstract

A characterization of finitely generated torsion modules of not necessarily finite projective dimension over a Cohen–Macaulay ring, is given in terms of the non-Cohen–Macaulay loci and the Fitting invariants of a free resolution of such a module.

Key Words:

• Cohen–Macaulay module
• Depth of a module
• Minimal free resolution
• Projective dimension

2000 Mathematics Subject Classification:

• Primary 13C14
• Secondary 13C15, 13D02

ACKNOWLEDGMENTS

We are indebted to Professors Winfried Bruns and Peter Schenzel for their valuable comments in preparing the manuscript.

Supported by the Ministerio de Educación y Ciencia of Spain under grant #MTM2005–00173.