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“School of Mathematics”

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Paper   IPM / M / 15690
School of Mathematics
  Title:   A note on Abelian categories of cofinite modules
  Author(s):  Kamal Bahmanpour
  Status:   Published
  Journal: Comm. Algebra
  Vol.:  48
  Year:  2020
  Pages:   254-262
  Supported by:  IPM
  Abstract:
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 in []. Also, as an immediate consequence of this result it is shown that the category of all I-cofinite R-modules C(R,I)cof is an Abelian subcategory of the category of all R-modules, whenever q(I,R)�?�1. These assertions answer affirmatively a question raised by R. Hartshorne in [Affine duality and cofiniteness, Invent. Math. 9(1970), 145-164], in some special cases.

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