Cofiniteness of Generalized Local Cohomology Modules Over Local Rings

Let Formula: see text be a local commutative Noetherian ring and Formula: see text an ideal of Formula: see text Assume that Formula: see text is a finitely generated Formula: see text-module of finite projective dimension Formula: see text and Formula: see text is a finitely generated Formula: see text-module of dimension Formula: see text We prove that Formula: see text is Artinian. Moreover, if Formula: see text is finitely generated, then Formula: see text is an Formula: see text-cofinite Formula: see text-module.