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- Title
Coartinianess of local homology modules for ideals of small dimension.
- Authors
Shen, Jingwen; Zhang, Pinger; Yang, Xiaoyan
- Abstract
Let be an ideal of a commutative noetherian ring R and M an R -module with Cosupport in V (). We show that M is -coartinian if and only if Ext R i (R / , M) is artinian for all 0 ≤ i ≤ cd (, M) , which provides finite steps to examine -coartinianess. We also consider the duality of Hartshorne's questions: for which rings R and ideals are the modules H i (M) -coartinian for every artinian R -module M and all i ≥ 0 ; whether the category (R ,) coa of -coartinian modules is an abelian subcategory of the category of R -modules, and establish affirmative answers to these questions in the case cd (, R) ≤ 1 and dim R / ≤ 1.
- Subjects
ARTIN rings; ABELIAN categories; COMMUTATIVE rings; NOETHERIAN rings
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 10, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823502122