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.