2013/08/28 by Kamal Bahmanpour, Bahmanpour, Kamal, Reza Naghipour +3
Computer Science · Mathematics · #13D45 #13E05 #14B15 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1308.6040
openalex publication_date 2013/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R denote a commutative Noetherian (not necessarily local) ring, M an arbitrary R-module and I an ideal of R of dimension one. It is shown that the R-module \ExtiR(R/I,M) is finitely generated (resp. weakly Laskerian) for all i≤ \rm cd(I,M)+1 if and only if the local cohomology module HiI(M) is I-cofinite (resp. I-weakly cofinite) for all i. Also, we show that when I is an arbitrary ideal and M is finitely generated module such that the R-module HiI(M) is weakly Laskerian for all i≤ t-1, then HiI(M) is I-cofinite for all i≤ t-1 and for any minimax submodule K of HtI(M), the R-modules \HomR(R/I, HtI(M)/K) and \Ext1R(R/I, HtI(M)/K) are finitely generated, where t is a non-negative integer. This generalizes the main result of Bahmanpour-Naghipour \citeBN and Brodmann and Lashgari \citeBL.