On the Finiteness Properties of U_iAss_RExt_Rⁿ(R/α^I, M)

ABSTRACT

Let 𝔞 be an ideal of a commutative Noetherian local ring R and let M be a finitely generated R-module. Let n be a positive integer such that the support of local cohomology module is finite for all i < n. In this note we show that the set

is finite. Also we determine precisely the associated prime ideals 𝔭 of satisfying dim R/𝔭 > 1.

Key Words:

• Filter regular sequences
• Generalized regular sequences
• Local cohomology modules
• Support of local cohomology modules

2000 Mathematics Subject Classification:

• 13D45
• 13E05

ACKNOWLEDGMENTS

The author is deeply grateful to the referee for careful reading of the manuscript and helpful suggestions. The author was partially supported by a grant from Institute for Studies in Theoretical Physics and Mathematics (IPM) Iran (No. 83130024).

Notes

Communicated by I. Swanson.