2014/06/05 by Davood Asadollahi, Asadollahi, Davood, Reza Naghipour +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC
paper · pdf · doi:10.48550/arxiv.1406.1323
9 pages
openalex publication_date 2014/06/05 · arxiv created 2014/06/16 · arxiv updated 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R denote a commutative Noetherian ring. Brodmann et al. defined and studied the concept of the local-global principle for annihilation of local cohomology modules at level r∈ℕ for the ideals \frak a and \frak b of R. It was shown that this principle holds at levels 1,2, over R and at all levels whenever dim R≤ 4. The goal of this paper is to show that, if the set \AssR(H\fa^f\fa\fb(M)(M)) is finite or f\fa(M)≠ c\fa\fb(M), then the local-global principle holds at all levels r∈ℕ0, for all ideals \fa, \fb of R and each finitely generated R-module M, where c\fa\fb(M) denotes the first non \fb-cofiniteness of local cohomology module Hi\fa(M). As a consequence of this, we provide a new and short proof of the Faltings' local-global principle for finiteness dimensions. Also, several new results concerning the finiteness dimensions are given.