2022/02/19 by Glenn Ando, Ando, Glenn
Mathematics · #Algebra over a field #Algebraic structures and combinatorial models #Annihilator #Combinatorics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Image (mathematics) #Lambda #Mathematics #Physics #Pure mathematics #Ring (chemistry) #math.AC
paper · pdf · doi:10.48550/arxiv.2202.09528
12 pages
arxiv created 2022/02/19 · openalex publication_date 2022/02/19 · arxiv updated 2022/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Faltings' annihilator theorem is an important result in local cohomology theory. Recently, Doustimehr and Naghipour generalized the Falitings' annihilator theorem. They proved that if R is a homomorphic image of a Gorenstein ring, then f_\mathfraka^\mathfrakb(M)n = λ_\mathfraka^\mathfrakb(M)n, where f_\mathfraka^\mathfrakb(M)n := inf\i ∈ ℕ | dimSupp(\mathfrakbt H_\mathfrakai(M)) ≥ n for all t∈ ℕ\ and λ_\mathfraka^\mathfrakb(M)n := inf\λ_\mathfraka R_\mathfrakp^\mathfrakb R_\mathfrakp(M_\mathfrakp) | \mathfrakp\inSpecR with dimR/\mathfrakp ≥ n\. In this paper, we study the relation between f_\mathfraka^\mathfrakb(M)n and λ_\mathfraka^\mathfrakb(M)n, and prove that if R is an almost Cohen-Macaulay ring, then f_\mathfraka^\mathfrakb(M)n ≥ λ_\mathfraka^\mathfrakb(M)n - cmdR. Using this result, we prove that if R is a homomorphic image of a Cohen-Macaulay ring, then f_\mathfraka^\mathfrakb(M)n = λ_\mathfraka^\mathfrakb(M)n.