2015/04/05 by V. Erdoǧdu, Erdoǧdu, Vahap, Tuğba Yıldırım +1
Computer Science · Mathematics · Medicine · #13D45 #14F17 #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1504.01148
openalex publication_date 2015/04/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Let R be a Noetherian ring, I an ideal of R and M an R-module with cd(I,M)=c. In this article, we first show that there exists a descending chain of ideals I=Ic\supsetneq Ic-1\supsetneq ⋯ \supsetneq I0 of R such that for each 0≤ i≤ c-1, cd(Ii,M)=i and that the top local cohomology module HiIi(M) is not Artinian. We then give sufficient conditions for a non-negative integer t to be a lower bound for cd(I,M) and use this to conclude that in non-catenary Noetherian local integral domains, there exist prime ideals that are not set theoretic complete intersection. Finally, we set conditions which determine whether or not a top local cohomology module is Artinian.