A Note on Abelian Categories of Cofinite Modules

Let R be a commutative Noetherian ring and I be an ideal of R. In this article, we answer affirmatively a question raised by the present author. Also, as a consequence, it is shown that the category of all I-cofinite R-modules is an Abelian subcategory of the category of all R-modules, whenever Thes...

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Bibliographic Details
Published inCommunications in algebra Vol. 48; no. 1; pp. 254 - 262
Main Author Bahmanpour, Kamal
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2020
Taylor & Francis Ltd
Subjects
Abelian category
cofinite module
cohomological dimension
local cohomology
Modules
Noetherian ring
Primary 13D45
Questions
Secondary 14B15
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Summary:Let R be a commutative Noetherian ring and I be an ideal of R. In this article, we answer affirmatively a question raised by the present author. Also, as a consequence, it is shown that the category of all I-cofinite R-modules is an Abelian subcategory of the category of all R-modules, whenever These assertions also answer affirmatively a question raised by R. Hartshorne, in some special cases.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2019.1640238