On the generalization of Faltings' Annihilator Theorem

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Let R be a commutative Noetherian ring and let n be a non-negative integer. In this article, by using the theory of Gorenstein dimensions, it is shown that whenever R is a homomorphic image of a Noetherian Gorenstein ring, then the invariants {i∈₀| (ᵗHⁱ(M))≥ nfor all t∈₀} and {λ R R(M)|∈ Spec R and R/ ≥ n} are equal, for every finitely generated R-module M and for every ideals a, b of R with b a. This generalizes the Faltings' Annihilator Theorem [G. Faltings, Über die Annulatoren lokaler Kohomologiegruppen, Arch. Math. 30 (1978) 473-476].