Some equivalent conditions for Huneke's two conjectures

Abstract

In this paper we give some equivalent conditions for the C. Huneke's two conjectures concerning the finiteness properties of the local cohomology module Hⁱ_I (R), where R is a regular local ring, I is an ideal of R and i ≥ 0 is an integer.

Mathematics Subject Classification (2010): 13D45, 14B15, 13E05.

Keywords: Bass number, Betti number, Goldie dimension, local cohomology, regular ring