2021/10/25 by Jingwen Shen, Shen, Jingwen, Pinger Zhang +3
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2110.12718
openalex publication_date 2021/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathfraka be an ideal of a commutative noetherian ring R and M an R-module with Cosupport in V(\mathfraka). We show that M is \mathfraka-coartinian if and only if ExtRi(R/\mathfraka,M) is artinian for all 0≤ i≤ cd(\mathfraka,M), which provides a computable finitely many steps to examine \mathfraka-coartinianness. We also consider the duality of Hartshorne's questions: for which rings R and ideals \mathfraka are the modules H^\mathfrakai(M) \mathfraka-coartinian for all i≥ 0; whether the category C(R,\mathfraka)coa of \mathfraka-coartinian modules is an Abelian subcategory of the category of all R-modules, and establish affirmative answers to these questions in the case cd(\mathfraka,R)≤ 1 and dimR/\mathfraka≤ 1.