ON THE FINITENESS OF BASS NUMBERS OF LOCAL COHOMOLOGY MODULES

Abstract

Let R be a commutative regular ring of dimension d, I be an ideal of R and M be a non-zero finitely generated R-module. In this paper we show that Huneke's two different conjectures are equivalent. Also we provide some partially affirmative answers to them. In fact it is shown that the Bass numbers of [Formula: see text] are finite for all i ≥ 0, whenever d ≤ 3. Also if (R, m) be regular local ring, we show that the Bass numbers [Formula: see text] are finite, for all i ≥ 0 and all j ≥ 0, and [Formula: see text], for all i ≥ 0 and all j ≥ 0, whenever height(I) = 1.