On the generalized local cohomology of minimax modules

Abstract

Let [Formula: see text] be a commutative Noetherian ring with identity and [Formula: see text] be an ideal of [Formula: see text]. Assume that [Formula: see text] is a finite [Formula: see text]-module and [Formula: see text] and [Formula: see text] are minimax [Formula: see text]-modules such that [Formula: see text]. In this paper, among other things, we show that [Formula: see text] is minimax for all [Formula: see text] and [Formula: see text] when one of the following conditions holds: [Formula: see text](i) [Formula: see text]; [Formula: see text] (ii) [Formula: see text]; or (iii) [Formula: see text]. As a consequence, we obtain that the Bass numbers and Betti numbers of [Formula: see text] are finite for all [Formula: see text] when one of the above conditions holds.