{"paper":{"title":"On the generalization of Faltings' Annihilator Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mohammad Reza Doustimehr, Reza Naghipour","submitted_at":"2013-08-27T18:45:43Z","abstract_excerpt":"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 $\\inf\\{i\\in\\nat_0|\\, {\\dim\\Supp}(\\fb^tH_{\\fa}^i(M))\\geq n\\text{for all} t\\in\\nat_0\\}$ and $\\inf\\{\\lambda_{\\fa R_{\\p}}^{\\fb R_{\\p}}(M_{\\p})|\\,\\p\\in {\\rm Spec} \\, R \\text{and} \\dim R/ \\p\\geq n\\}$ are equal, for every finitely generated $R$-module $M$ and for every ideals $\\frak a, \\frak b$ of $R$ with $\\frak b\\subseteq \\frak a$. This generalizes the F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5945","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}