Let (R,m) be aNoetherian local ring and a be an ideal of R. Suppose that height (a ˆR + P)/P ≤ 1, for every P ∈ Spec ˆR. In this paper, it is shown that the category of acofinite modules forms an Abelian subcategory of the category of all R-modules. This assertion provides a partially affirmative answer to a question raised by R. Hartshorne in [Affine duality and cofiniteness, Invent. Math. 9 (1970), 145-164].
