ON GENERALIZED REGULAR SEQUENCES AND THE FINITENESS FOR ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES

Abstract

Let (R, 𝔪) be a Noetherian local ring and M a finitely generated R -module. The two notions of generalized regular sequence and generalized depth are introduced as extensions of the known notions of regular sequence and depth, respectively. Some properties of generalized regular sequence and generalized depth, which are closely related to those of regular sequence and depth, are given. If x₁ ,…, x_r is a generalized regular sequence of M , then

is a finite set. Some finiteness properties for associated primes of local cohomology modules are presented.

Key Words:

• Generalized depth
• Generalized regular sequences
• Local cohomology modules

AMS Classification:

• 13D45
• 13C15

ACKNOWLEDGMENT

I am grateful to Professor N. T. Cuong for useful suggestion. I thank the referee for helpful comments, and the ICTP, Trieste, Italy, for the financial support.

Notes

^#Communicated by I. Swanson.