COFINITE MODULES

Abstract

The R-module M is called a FA module if there exists finite submodule N such that M/N is Artinian, and is called an AF module if there exists Artinian submodule A such that M/A is finite. We show that if M and K are FA (or AF) modules with Supp(K) ⊆ V() then Ext ⁱ _R (K, H ^j (M)) is finite for all i ≥ 0 and j > 0, if R is local and is an ideal of dimension one or principal.

Keywords:

• Local cohomology
• Cofinite module
• Associated primes
• 1991 Mathematics Subject Classification: 13D45, 13C99, 13C05

ACKNOWLEDGMENT

This work was done when the author was visiting the Abdus salam International Centre for Theoretical Physics, Trieste, Italy, as a regular associate member. The authors would like to thank the University of Tehran for partial support. This research was in part supported by a grant from the Institute for IPM.