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 C(R, l)(cof) is an Abelian subcategory of the category of all R-modules, whenever q(I, R) <= 1: These assertions also answer affirmatively a question raised by R. Hartshorne, in some special cases.