Generalized F-Modules and the Associated Primes of Local Cohomology Modules

ABSTRACT

We introduce a class of modules called generalized f-modules, which contains strictly all f-modules and generalized Cohen–Macaulay modules. The properties of multiplicity, local cohomology modules, localization, completion… of these modules are presented. A result concerning the finiteness of associated primes of local cohomology modules with respect to generalized f-modules is given. Some connections to the coordinate rings of algebraic varieties and Stanley-Reisner rings are considered.

Key Words:

• Associated primes
• Generalized f-modules
• Noetherian dimension

Mathematics Subject Classification:

• 13D45
• 13C15

ACKNOWLEDGMENT

The authors thank Prof. Nguyen Tu Cuong for many useful suggestions. They thank the referee for helpful comments. The first author is grateful to Institute Fourier (Grenoble, France) for the support during the academic year 2003-2004 when this article was completed.

Notes

Communicated by A. Facchini.