Abstract
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 \({\inf\{i \in \mathbb{N}_0|\, \rm{dim\, Supp}(\mathfrak{b}^t H_{\mathfrak{a}}^i(M)) \geq n\, \rm{for\, all}\, t \in \mathbb{N}_0\}}\) and \({\inf\{\lambda_{\mathfrak{a} R_{\mathfrak{p}}}^{\mathfrak{b} R_{\mathfrak{p}}}(M_{\mathfrak{p}})|\, \mathfrak{p} \in {\rm Spec} \, R\, \rm{and\, dim}\, R/ \mathfrak{p} \geq n\}}\) are equal, for every finitely generated R-module M and for all ideals \({\mathfrak{a}, \mathfrak{b}}\) of R with \({\mathfrak{b}\subseteq \mathfrak{a}}\). This generalizes Faltings’ Annihilator Theorem (see [6]).
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Dedicated to Professor Jürgen Herzog
This research was in part supported by a grant from IPM.
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Doustimehr, M.R., Naghipour, R. On the generalization of Faltings’ Annihilator Theorem. Arch. Math. 102, 15–23 (2014). https://doi.org/10.1007/s00013-013-0601-5
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DOI: https://doi.org/10.1007/s00013-013-0601-5